I have an '83, and out of the factory it had all that wannabe smog crap on it, but the stuff never really did anything but rob HP and take up room, so out it went. I later swapped the dying 305 for a 350, and again ran everything without the aid of the "computer" (it is actually completely disconnected now). The swap was simple as pie, as far as the engine goes, but the trannies in 3rd gens of that year are absolute chunks, so you will probably want to do a tranny swap while you are at it; get a nice TH-350 rebuilt, they are affordable enough.
Basically, once you get the engine in there, some minor things need to be done, like spiff up the exhaust to allow the new engine to work right. A true dual exhaust is very tough, and a lot of shops will say it is impossible, but I know how to do it. I won't get into that now though. About the carb, the stock 4 bbl q-jet worked very well on my 350 until it wore out and was replaced with a Holley.
If you do the swap and remove that bogus smog stuff (if it hasn't already been taken out), then you may find some "check engine" lights staying on, so just pull the bulbs, the computer is now HAL 2000: completely useless. GM made a very weak attempt in the early 3rd gens to provide some sort of smog control system, but really it did little more than simply blow air into the exhaust with a pump to dilute it. It is otherwise completely ineffective at doing anything.
Engine choice is something I suppose I should mention. Get a used engine to start, preferably one you can hear running. Aim for something late 70's so there won't be any smog crap to worry about, and try to pull it from a granny car like a sedan. This will pretty much guarantee it has not already been rebuilt and oversized, which will come in handy down the road someday when you eventually will want to rebuild it (and trust me, you WILL want to, it is in your blood to do so). The nice thing about buying the whole engine as a unti is that everything is there already, chiefly the heads are what you are after since 305 heads don't jive on a 350. Now, this will have cost you about $500 for the engine if you have played your cards right. If you want to throw some performance into it, you may invest in a mild/moderate cam, a good timing set, and perhaps an aftermarket intake, but definately cam and timing set. I say this because you can bolt on things like intakes and carbs later down the road while the engine is still in the car, cams you can't, and timing sets are not expensive and go hand in hand with a fresh cam. Then focus on the exhaust. Again, the exaust is something that can be worked on after the engine is in, so it isn't an absolute must right at the moment, you can still have fun driving while you save up some more $.
Ok, that about sums it up. I'll shut up now after having told you my life story, heheh.