i vote for doing a 5 speed swap (or 6 speed if you can afford it) , using your original 2.8L motor, then spending the rest on mods.. s52 cams, injectors, OBDI ecu, CAI, m50 manifold, headers, exhaust.
that will put you between around 250 - 270HP.
I bet even that will end up pushing you over your budget. i highly doubt that you will be able to do the M3 swap including a tranny and diff, that will probably push you over the limit cash wise.
Also, why do this swap to a 2.8L? sell it and pick up a 325 for less money and you will have more cash for the swap.
IMO doing this to a car that was originally a 2.8L that was running fine is a huge waste engine wise and financially.