LT1/L99 didn't make it into B-bodies until 1994... at least from the factory.
Yours would have come with a TBI.
There is power to be had in the 350, but you're looking at a complete re-do. TBI 350s were all well-matched for the 190hp they made, so its not like you can just swap cams, heads, or put headers on it and release the magic genie from the lamp. TBIs had dished pistons, the worst-flowing production heads Chevy ever put on a V8 (and that even includes all the way back to the old-school 50s heads), tiny cams (180s intake duration and 116 LSA), low compression.... its a whole package of well-matched smog-legal goodness. You will also find that from 87-93, Chevy did some fun mix-n-match as they transitioned over to the newer generation of small blocks (94-97 Vortec). In most of the trucks you'll find a block with roller cam provisions (taller lifter bores and bosses for the spider retainer) but nearly all of them got flat cams. In cars, there were more roller cams, but its not a guarantee. If you pull the intake and don't see a roller-ready block, sell it. Seriously. There is no reason in 2018 to build a flat-cam engine, and roller conversions are expensive. (special lifters, dog bones, etc. Think $1000 for a conversion cam kit instead of $150 for just a cam).
So, if you pull the intake and see a roller block, it's worthy of using, however you'll need a clean-slate rotating block. You can basically keep the block, crank, and rods, but everything else will need to be something else if you want to make power. My go-to recipe for a 300-325 hp small block is aftermarket Summit iron Vortec heads, vortec carb intake (ZZ4 intake is expensive, but look to marine carbed intakes from a boat boneyard... same intake casting with bronze-lined coolant crossover and often $20). flat-top pistons with valve reliefs, and a Melling cam. I'm trying to think of the cam number. I think its 22124, but I might be remembering the flat cam part number. Its something like 194/208 duration on a 112 LSA IIRC. It can use stock valve springs from a roller application, but they might start to float at about 5200. If you don't get the aftermarket Vortecs, make sure to get a retainer kit that allows for .550" lift. Stock Vortecs are only good to about .470". That will get you a 9.5:1 assembly that will easily take 87 octane and make around 300 hp.
If you live in smog territory, you can easily keep it TBI, but take your TBI and smash it with a large granite rock. Or sell it to someone who still thinks they are worth something. (can you tell I hate the small block TBI?). Instead, replace it with a BBC TBI. They are actually decent-ish. Well, they still suck in my opinion, but they at least flow a decent amount. An unsuspecting inspector (say that ten times fast) will never notice a thing. If you live in a place that does a sniffer test, you should be able to tune it to pass a tailpipe test with a good chip burner.
If you don't want to put all of that money and effort into a SBC, there is a lot of aftermarket support for LS swaps. Even if you do have to smog, you can likely get by with it with a little redtape.
If you don't have to smog it, the world is your oyster. Caddy 500 weighs about the same as a 350 and makes mountains of torque. Mine was 390hp/5xxtq (dyno couldn't hold the torque, so it was probably north of 550 lbft) and got 18 mpg in a 66 Bonneville. I set redline at 4700 and used 2.93 gears and a TH400. Cruised all day at 1900 rpms and roasted tires.
Duramax would be killer. Probably get 30 mpgs in that wagon.