Nice find! I've got an 03 325i myself.
My only advice would be to do all preventative maintenance and check ups before getting into any mods. I drive mine bone stock since it's just my daily and I don't track/go nuts. The e46 generation BMW's are so damn cheap on the used market because while the engines themselves are fairly solid, the accessories under the hood are cheap plastic and turn to glass after 100,000 miles. Meaning, people don't spend the money every 80-100k miles to do the cooling system overhaul or VANOS solenoid repair, so even though it might run fine, a good 60% of them are just about to be knocking on death's door. They reallllllly don't like any type of overheating, the engines will take most anything thrown at them but if you start getting hot, shit starts warping and you're looking at double the cost of the car for a new drivetrain.
Check the water pump, all radiator hoses, thermostat, do a compression check, get the VANOs checked out. If you do the work yourself it won't be too expensive, which is the key to keeping an older BMW on the road without going for broke. I bought mine 3 years ago for about the same price as you, spent another $700 on parts for the cooling system and a new MAF, took me the weekend to do it all myself, and it's been great ever since outside of normal oil/tires/brakes.
If you take the precautionary measures, it's an absolutely amazing car for the cheap, sadly most owners don't and that's why they're all so cheap
Edit: If shit does go wrong and it turns into a lemon, LS Swap it and be the coolest and most hated person at the track.