I did it with an SBF, also with the goal of keeping the budget really small.
Headers on the driver's side are the hitch. They wind up close to the ABS pump. I moved mine to the front of the engine bay. The steering shaft has a big meltable rubber rag joint to the rack. I replaced that with a joint that Flaming River sells specifically for the E36 rack. With those out of the way, all you need to do is weld up a header that will fit in the remaining space. I also tried to use the stock cats and muffler, but they were holding me back a bit with just a stock SBF, so I did dual 2.5" replacements this winter.
The differential is a 4-hole bolt plate and the E36 uses a two-piece drive shaft. Some people take the back end of the E36 shaft and whatever slip-yoke shaft they have for the Chevy to a shaft shop for welding into a 1-piece unit. Others find an adapter plate that converts the dif to a standard 1310 U joint. Jags That Run sells those, but they may be out of stock sometimes. There is also a fair amount of dinking around to get the drivetrain angles within the range of tolerable. There's enough drop from the trans to the diff for the u joints, but the transmission angle is tough to get right without hitting the steering rack with the oil pan. That may just be an SBF problem though because the intake manifold is so tall.
I dunno about the Chevy oil pan but I think you're on the right track with rear sump. That's what I use for the SBF.
I re-used the E36 power steering setup and made a bracket to get it on the engine. If you need AC, you will have that problem plus no flexibility where to put the compressor.
The reason all those E36s have engine problems is the cooling system. Best to get a new radiator and pusher fan in there, but there's a fair amount of room.
I don't know how much fuel flow you would need for the 350. It's pretty much impossible to find a good estimate of the E36 stock pump LPH capacity but for anything much over 250hp, plan on upgrading to a Walbro in-tank. I am trying to buck up the voltage to the stock pump instead, just to see if I can make it work.
Brakes would be fine for the street but not for the track unless you used an M3 chassis. I tried the stock non-M setup and it wasn't up to track work once the horsepower was upgraded. I swapped in front calipers and rotors from an e46 330i and rear calipers/rotors from an E46 325i, which worked great, no need to change the master cylinder. But the upgrade means 17" wheels too. Tire Rack has some decent TR Motorsport jobs for about $150/corner.
Only other problem is the suspensions on these cars are really soft for track work and the bushings are all shot, so there is a lot of work and replacement parts right there. But there's also a steady supply of quality used coilovers and such for sale at Bimmerforums.