negatives are 80's gm electronics in a sub 3k car. You will be having problems. Specific parts such as dash, bose radio's, auto a/c controllers etc can be expensive to repair/replace, but may be fixed with a little knowledge, and aren't that vital. If your not scared of a parts interchange book you can find the same parts for less $$ on many items.
In my opinion I would suggest a 6 speed car, tpi is good for mileage and AX, lt1 is nice, but probably not for 3k.
window seals can rot/be bad and leak, probably about $500 in parts, need to be fixed so wiring doesn't rot. Tires and wheel bearings are expensive, autocrossing will eat both.
The history of repairs/upkeep should let you decide if its an ok dd, my 89 strangely enough has become my "reliable" car now.. The GM multronic (grey) fuel injectors tend to be a problem on all tpi's, easily replaced w/ford injectors. Other than that, its a 350. I'm working on modifying the ecm concerning what is a "lean burn" mode disabled in production but the code is still there. (I'm not responsible for it, its been done, I just mean I'm working on enabling it on my vette) Essentially under certain parameters it will lean out the mixture and advance the ignition to return better mileage at a sacrifice for pollutants (a hypothesized reason its not enabled). Right now with no modifications other than exhaust I average19-20 mpg in town and have got a tank of 30mpg on a road trip, usually average 25-26 on the highway. Its also easy to average 10 around town and do 180's with the gas and clutch b/c the turning radius is so big. Premium is important depending on setup, I get ALLOT of spark knock on 87 w/stock tune.
Clutch hydraulics are considered weak and problematic.
If your worried about the crossfire or tpi, think about an lt1 intake conversion, easy and cheap if you find a lt1 or even l99 in a j-yard (think Buick/caprice) To a large degree if you ignore the reverse coolant flow of the lt1 the L98 heads don't flow too differently, and have comparable results with the lt1. its still a 350.
Or if its that bad, carb intake, drop all electronics, fab up some gauges and loose some weight. It is still a galvenized steel frame with fancy 4wheel independent suspension, big brakes which are easily upgradeable (abs problems can be expensive however) and a "fiberglass or plastic" body. Ride is pretty rough on rough roads, cabin is "cozy" bottoms out on everything but I think it rides great if you have decent roads.
You most likely wont just get in and have a dd c4 for 3k, but it shouldn't be that hard to keep it a dd w/little $$. Even if you get beat by slammed hondas, the ladies generally prefer the 'vette.