are you referring to the classic 350 small block or an Ls1? an ls1 would have potential, but a classic 350 might not be worth the effort and cost for swapping it in. as stated, buying the K member will save alot of headaches.
what is the situation that calls for it? or the driving desire?
My take on this... if the 388 is carbed you would need a kmember&possible suspension changes, fuel system, possibly cowl hood, and lots of odds and ends depending what accessories you want to run, etc. This could add up to some $$.
If the 388 is an EFI system, then you will need on top of the above, wiring and engine management/controls, so lots of $$ from above plus even more $$ for the EFI bits.
Both cases likely need a trans/trans work/modification to get that sorted as well...meaning driveshaft also...
In either case, the cost to bastardize your 02 with a chevy engine, is IMO far more than the cost of getting a decent used running 4.6 2V (I'm assuming you have a GT...if you have a V6 then there are even more things that for sure need changed (rear axle to handle the power (7.5 to 8.8), V8 springs vs. V6 springs to handle added front end weight, etc. etc.)
IMO the cost of this swap is very prohibitive, even if the engine is free. You are much better off getting a decent running 4.6 2V or rebuilding your current one, than putting that 388 in the car. A proper K member setup alone is going to be atleast $1k with the bare minimum, to do it right you probably need close to $2k or more in just suspension parts...