You are certainly lucking out on advice here -- 3 Series forum would tell you to search more. I'll chime in.
The ER Competition Oil Cooler setup is definitely expensive, but it works, and bolts up, comes with everything you need. I don't like that it doesn't include a remote thermostat, meaning if you keep your stock oil theromstat, you're still starting your runs around 240*. Adding in a remote setup wouldn't be too hard. Alternatively, you can bypass the thermostat with something like the BMS Sport Oil Cooler Valve (bullshit for thermo delete.) If you don't daily drive your car, you can get away with this, but it's not ideal.
I'm building my own dual core setup to run in sequence, similar to the ER, only with a 185* remote thermostat and big -10AN line. Mine will need a few simple custom brackets to mount, and won't come with shrouds, but I have a feeling it'll match or outperform the ER and all in, I got the parts for $800.
Stock radiator is OK on this car, but I'd advise the CSF radiator. Not sure on the cost of the 1M aux kit with fan, but the CSF is bulletproof, even when your oil temps and IATs are overcooked. Over 20 minutes on Laguna Seca and my water temp never passed 230*, even with oil at 280*.
I'd go Wavetrac over MFactory. OSG and Quaife are also good. You can check out
www.diffsonline.com and order a complete pumpkin to make it an easy swap. If you don't mind spending some more, you can upgrade to a 3.48 final drive vs the stock 3.08. It'll make the car feel way sportier and more lively. You'll lose some rpm on the highway though. I had a Wavetrac in my 335i and just ordered a new one with the 3.48 for the 1.
Get some track pads and good rotors / lines / fluid. The brakes look nice but they aren't really that great. Good for now though. Wait till you find your limit.
A square 17x8.5 or 18x8.5" wheel setup with 245 or 255s all around will help your cause a lot, but this should be done in conjunction with proper coilovers, camber plates (KW Clubsports come with everything), M3 arms, M3 front sway and rear subframe and diff bushings like everyone said.
If you want quicker steering you can also look out for an M3 steering rack. Just ordered one on eBay for $450. Steering will be way heavier, but more suited to track driving with a 12.5:1 ratio vs the stock 16:1. 1M came with this rack as well, only we don't have servotronic to assist with the weight at low speeds. You'll get used to it.
Good luck and have fun.