Some people don't want to read tho, they want the hold my hand every step of the way method.Or, here me out., you said your budget is $2500 so Just put that known running engine in, because every bit of that is gonna be spent in other places just to get any gen3/4 in the car. Fuel system, wiring, engine mounts, crossmember, cooling,exhaust, trans lines_cooler, tune, driveshaft for a stock swap.
Once you get it in, and running/driving. Then go to the junkyard and get an engine to do your total rebuild.
For your transmission if you don't feel comfortable rebuilding it just go to the yard and get 1 with red fluid that doesnt smell burnt. I've had no issues doing this on daily drivers.
You'll spend 2500+ on a total rebuild.
If your gonna go thru with the ls swap here's my advice, read,read,read, and then read some more. The info is there for you, but you have to go get it. Do your research or your car won't get off the jackstands
I charge hourly for that.