They're not going to have as much collector interest as a Camaro or a Malibu, but 427 Impalas definitely are worth money, especially if they were originally equipped with a four speed manual transmission. As mentioned, since the original engine is gone (and I assume there's no way to track it down) a small block Chevy would be the least expensive way to go and it can always be converted back to a big block in the future.
When I was a kid, one of my cousins bought a brand new 1967 427 Impala SS four speed, it looked just like this one:
It was a seriously cool car, and seriously fast.
If that thing came with a 427 you’d be nuts to put anything else in. I agree with the 454 comment though if cash is tight.
I am officially jealous!! I've never been much of a Chevy guy, most GM products just never did it for me styling-wise (Still true today) but the 2 exceptions are the C2 Corvette and the 4th gen (65-70) Impala. The C2 Corvette is, in my humble opinion, the most beautiful car GM ever made, but a close second is the 1965 Impala. All the 4th gen Impalas are beautiful, long low and wide. Your 69 can be beautiful again, but that 65, with those 6 round tail lights......pure automotive artwork. 
Love 'em!!
If it were mine, and I could afford it, I'd go with one of the LS variants. I do get a little jaded about them, because they seem to be some people's answer to everything. Weed eater need more power? LS Swap. Need to make your washing machine faster? LS swap. 
Not throwing rocks, I'm just one who never seems to go along with the majority. I like unusual, and odd. But, that's just me. There is no denying that the LS series of engines are absolutely fantastic just about any way you look at it. Reliable, long-lasting, powerful, relatively inexpensive considering what you get for your $$ and HUGE aftermarket support. You name it and someone has probably already put an LS in it. You spend more than you would putting in a SBC, but probably quite a bit less than going with a 427. Particularly in a HP per dollar comparison, to say nothing of fuel economy and overall drivability. ( I do agree with the poster who said to use a 454 if you decide you just have to have a big-block, way cheaper and it'll look and sound pretty much the same) The LS, particularly with a modern transmission behind it, will give you a driveline that is much easier to live with day to day.
Looking forward to seeing your progression on that big, lovely old boat whatever you choose. I'm just throwing out my $.02 because I love those old Impalas so much..... 
If you can afford the BBC, build a 496. The kits are cheaper and they are internally balanced. Dollar for dollar this is the easiest cheapest BBC to build. We own a 427, 468, 496, 502 and a 525. We are big BBC fans. We also have a dozen SBCs. From 260 to 436 CI. But if I were building the car, it would get an LS. You won't be disappointed. 6.0L with a small cam and a good tune. You'll be bucks ahead and you'll wonder why you didn't do it sooner.
If it was a factory 427 --might make sense to get another 427.
Otherwise, easiest and fastest to get a crate motor from Summit. Machine shop costs, replacement parts , plus the core engine add up really quick.
Usually if someone yanked out the 427 from an original 427 impala, the rest of the car was pretty used up.
So...
1.brakes
2.suspension
3.steering
4.electrical system
need some attention too...just other items to add into the spreadsheet...
The cheapest and easiest way to get this done is going to be with a small block and a carburetor.
BBC will be just as easy, but not quite as cheap.
If you want to dip your toe into the fuel injection pool, you might consider buying mid-80s to mid-90s TBI (throttle body injection) donor truck (it won't be a hotrod but you get the easy-starting pleasure of fuel injection). For a cruiser/driver it would be a cheap way to go...one of many)
An "LS" swap (used ubiuqitously for GM's Gen3 small block) gets mentioned often by people who haven't done it. I also haven't done it...but I've considered it on several projects and have not yet gone down that path. It's a great option for power and drivability, but you really have to spend money and/or have some time and skills and lots of patience for scrounging. I'm guessing this car can utilize truck intake and exhaust manifolds, accessory drive, and oil pan. If that's the case...it really won't be terrible (buying a wrecked truck donor vehicle is the most affordable way to come up with everything you need in my opinion...so if you can use all those truck pieces, that's good!).
But who's going to do this swap? It's not the kind of thing you're going to want to pay someone else to do. Labor costs on something like this would be staggering. If you can do it yourself and/or with the help of knowledgeable friends...that's how these sorts of projects typically can be accomplished somewhat affordably.
The car is going to need a high pressure fuel system and a wiring harness to run the fuel injection. This stuff is doable and available...but it REALLY starts to add up. I'd strongly urge you to make a list of EVERYTHING that would have to be done to convert this car to an LS engine (or any fuel injected engine, for that matter) and add up the costs of parts.
It can totally be done...but you want to make sure you know what you're in for. Many projects start off with good intentions and then get sold (to guys like me and others here) for pennies on the dollar when folks find out how much it's really going to cost to totally finish the project.
So after reading all of your very helpful comments and talking it out with my son (who has absolutely zero interest in cars), the plan is to go with the small block 350 in the Impala to get it going, and when I move on to my second project car, save up for a 427 for the Impala and pull the 350 to use in the new project car. Going with carburetor instead of fuel injected, and a manual transmission. I'm definitely doing a crate engine as opposed to assembling individual parts or trying to rebuild one from a junkyard.
I totally understand the costs of this project and estimate it in the $20,000 range, and to me it's completely worth it; my life choices are driven by "because I want to", "because I can", and "because I want to see if I can do it", and rebuilding a car on my own is up there on my list. It's a self-esteem thing, as well as to totally piss off my siblings who are of the opinion that I can't do a damned thing.
A couple of things to consider with a car of this vintage is that many of the systems are substandard compared to modern cars all of these systems are almost 50 years old. By systems I'm referring to braking, cooling, charging, electrical, fuel, HVAC, steering, suspension, etc. They've seen 50 years of wear and tear and more than likely modifications/repairs which may have been done right or not so much. Even if functioning correctly, a manual brake car with four wheel drums, like my 1969 Cougar (restomod driver), was a whole new eye-opening world to me compared to a modern power 4 wheel disc brake equipped car. To be a safe and reliable driver these all need to be investigated and may need to be fixed. On my driver condition Cougar I've replaced the entire cooling system, exhaust system, charging system, fuel system (converted to fuel injection), much of the interior, heater core and blower motor which required me to remove the entire dashboard. This winter is brakes, steering, transmission, and suspension.
I'd suggest reviewing some of the old car threads here for some insight and challenges. I've got one, snailmont5oh ('71 Ford station wagon), usernametaken (TVR), bobzilla (Chevy truck), pimpm3 (Corvair), MazDuece-Seth (International truck and Galaxy wagon now owned by Cotton), the V8kid (LS powered Nova) and many others. Many things to consider like tools (I had an extensive metric tool collection but limited SAE stuff), space (amazing how much room a dismantled car can consume), skills/hands-on assistance (my wife, kids, and Dad have all helped me a bunch-THANKS!), can all make things overwhelming at times. I'm not trying to be discouraging, just mentioning things that have impacted me on my projects over the years.
In reply to wawazat :
Not discouraging at all; as I've said, I love the classic feel but plan on modernizing it a bit. I've already taken into account that most of the remaining systems will probably need to be scrapped and purchased new, and maybe even updated/redesigned a little bit. I'm thankful to have a tribe here to help (of which I now consider all of you forum-goers here), such as my mom, who has 11 acres of land she's going to let me squat on should I get caught up on my bills first, and several friends to provide tools and muscle, both of which I'm in short supply of at the moment.
Hi Deanna! Welcome.
It's a great thing that you're going with the Carburated Chevy 350 first- not only are they extremely cheap with a massive aftermarket, but that also keeps you from having to change your fuel tank or suspension setup too heavily.
Firstly, resto-modding is awesome and for an old car like this, there has to be a junkyard source of upgrades for your old Impala. For example, most disc brake calipers from ~1990s Ford Mustangs fit onto their original ~1960s fathers with some custom brackets, which many forumites (and some companies) have made on the cheap. Better yet, things like Brake Boosters and radiators are mechanically simple when you understand how they work, and in the past 50 years have only become better- so I would join some facebook groups and specfic Impala forums and start asking for junkyarding information. There are plenty of cars from the 1990s that can yield powerful radiator fans, dependable relays, ect.
Oh, and look up an episode of Motor Trend's "Engine Masters"- they did an episode on a budget Chevy 350 a little while ago where they made a nice ~370 HP to the tire for a total cost (engine and all) of around ~$2,000 for cam, Vortec heads, carb, and intake. I'll try to find it.
Sounds like a good plan Deanna,
Way back around 1990: there was a 1969 formal roof 2D Impala for sale on US Rt1 south of Baltimore --faded/dull black paint/black interior, 327 engine, for $375...in a seedy neighborhood, car was run down but all there, I still think about that one sometimes...
meanwhile, here's an extended road test from 1968 of a 427 Impala vs the world (other big cars): 3800 lbs but no slouch at the drags!....
http://wildaboutcarsonline.com/members/AardvarkPublisherAttachments/9990486079155/1968-03_MT_1968_Impala_SS_Ford_XL_Sport_Fury_AMC_DPL_Test_1-8.pdf
