I bought one a couple years ago for all the reasons you mentioned, plus I love how they look, and sound, I cannot emphasize this last part, especially 1608 engines, but they all sound pretty close. Realistically you can get them to be very reliable but there are modifications required, I'll list what I've learned over the last 2 years restoring, modifying, and fixing mine...
Spider vs Miata Comparison:
My buddies all have NA/NB/NC Maitas and I've driven them all. As far as size, it's larger than an NA/NB (or at least feels like it) as there is ample width to the car, unlike say an NA, Alfa, MGB, Midget, which I was cross-shopping. You will learn to sit 'Italian' which basically means you're sitting on the floor with your arms at a funny angle to the steering wheel, at least I do at 5'10". I enjoy it more than a Miata because every drive is an adventure. I can't go anywhere without people coming over and talking to me about it, so expect some attention.
Handling is good for a 70s car, but it's nothing like modern cars, there's body flex, but it corners flat compared to larger 70s cars, and has some handling behaviors you will recognize as modern. Particularly when you get on it, it's very predictable.
Amenities are similar, without A/C, though later 80s cars can have it, but I've heard it's nothing great...
With the top up there's more space inside than an NA/NB/NC because there's a 'back-seat' though mine is long gone and it serves as a storage shelf, and maybe I'll build a stereo in there some day. If you want the top down, you'll quickly learn where Mazda took inspiration for the quickest, simplest folding roof in the world...
Mechanicals:
Brakes are 4 wheel disc but are so small and lightly boosted they won't stop you like a modern vehicle even if you mash it, but most of the time that's because the calipers need a rebuild, switch to ss brake lines to firm up the feel, some good pads and you'll be right as rain.
Transmission is a syncronized 5-speed with an un-syncronized reverse, so you'll learn quick to take your time when you want to back up. Also, watch for transmissions that 'pop' out of gear when in gear and unloaded, you'll need to rebuild if this is the case. Proper tension is also key to smooth shifts, too little and you'll grind, too much and you'll slip all day long. Also, the firewalls aren't well reinforced where the clutch cable goes through and they have a tendency to tear if they've lived in harsher climates where rust is a big issue.
Engines are great, even the late 70s 1800 smog cars can be made awesome by removing all the smog equipment. Personally I have a 1608 which is the rev-happy fun engine, not big power, and finicky when you fit a bigger carb, but damn fun. the 80s 2000 cars with fuel-injection are probably the best running, make good torque. The big things to watch are the timing belt which needs proper tension to keep cam timing (tricky the first time you replace it), valve shim clearance, which is easy to check and fix if there's a problem, and all the seals in the head of the engine since it's such a piece-meal head. For me, timing and fuel adjustments were my biggest hurdles to making the car run like I wanted it to.
Seals, just about every seal in this car (now i'm talking trans, diff, oil pan) was cork or paper from the factory, so even after you swap them out, expect some minor seepage, it comes with the territory, but if there are major leaks, get them taken care of fast. Some newer gasket kits are silicone/rubber which makes a world of difference, try to use these where possible.
Electricals:
Fuse block, double check it's all there, there are no melted wires (POs love to wire in stereos or DIY repair that damages things) and all the fuses are in-tact. Also check to see what works and doesn't. These cars aren't complex and the wiring schematics are in the Haynes manual in Black and white, or in color free online from Brad Artigue. I personally switched from the euro-style barrel fuses to ATO fuse block and fuses for simplicity. Most electrical problems can be traced to bad grounds, or dirty contacts which corrode over years of exposure. Early cars ground everywhere, later cars have a ground 'block' to put them all together. First thing is to clean all contacts, get some dielectric grease on there, that will help, alot.
Ignition, dizzy is simple, but older cars use mechanical points, there is a super simple $75-100 sensor that can replace this and make the ignition system one of the more reliable parts of the car, I highly recommend.
Alternators, have external voltage regulators, so if it goes bad, the only way to test it is on the car, but they usually don't.
Brown-wire fix. There is a problem with dim headlights and slow wipers, blinkers. It has to do with how the power is routed through the ignition switch, a simple fix is to add another larger gauge wire, it's documented all over so I won't bore you with details, but it will help many issues.
Cooling system:
Early cars have the T-stat in the head going to the radiator. These are fail-shut t-stats, which is bad. Later cars have a t-junction and an external t-stat, this is what you want to convert to, regardless.
All cars have the filler on the radiator, below the highest point in the engine/heater core coolant lines. The simplest fix is to go buy a t-junction (filler-flush T) and install it on the upper heater core outlet from the head to the fire-wall. This prevents having to jack the front end of the car up to bleed the system. I built mine from brass pipe-fittings from home-depot, $20, but it doesn't leak and will never crack like the plastic filler-flush Ts.
Radiators, are made of copper and tend to fail often, and are very expensive to replace, OEM are $500, to get it boiled and recored $300, to get it resealed can cost $100-200. I personally swapped to a universal 2-core aluminum and tossed the heavy old electric fan for a new light-weight ultra slim fan. I now have almost too much cooling, which is a good thing here in Georgia...
Rust:
The big one, check under the front along where the front sway-bar connects, if it's an older car with the battery in the engine bay (later 70s they moved to the trunk), check for rust near the shock tower. Expect rust under the valence between the hood and windshield where the fresh air cabin intakes and windshield wiper lives. There are 2 drain holes but they will rust, you can expect from inside the car under the dash laying on your back with a flashlight. Check the frame rails and the floor pans (pull up the carpet). Check along the bottoms of the doors (I just finished cutting out the cancer on the inside lower part of one door and welding in repairs, still have to fix the other, but it was very minor, no repaint on the outside, I've been lucky with mine). Check in the trunk, take out the mat and wood decking. Realistically if you want a Fiat, or any older car at sub $5k money, expect some rust somewhere. If you just want to bondo and paint, that's up to you. If it's only sheet metal (i.e. non-structural) and you don't know how to weld, I'd personally recommend investing in a cheap MIG welder (Hobart 140 springs to mind) and learn, it will serve you well, and really help the car. If there's holes in the frame rails, or any of the shock towers or severe rust in the floor pan area in general, I'd steer clear.
Summary:
I too like you started out here asking questions, cross-shopped lots of cars, and searched for over a year before I found this one and pulled the trigger. I personally think they're a highly underrated car and are tons of fun for very little $. You can get used parts over on the fiat spider board or mirafiori. If you want new parts there's tons of sources, AutoRicambi, Midwest-Bayless, Vicks, International-Auto-Parts, Mr. Fiat, Allison Automotive. There are many aftermarket sources and support is good. Just for reference I have less than $2300 in my car including purchase. The only things that I haven't restored is getting the wood panels for the dash, and hooking up the last few electrical indicators in the dash that were missing when I bought it. These cars are simple as dirt, and cheap to restore/fix, but hey, I'm a fanboi I guess.