I've been track driving for 11 years and have my SCCA and BMWCCA comp licenses for eight years.
To go really fast costs lots of money and there will always be someone with more money and will go faster LOL!
Most of the time, it's the driver mod that makes the biggest difference in lap times (especially if you're at a weekend "drivers school" like BMWCCA has or lapping days). You'll find plenty of "fast" cars not going much quicker than our modified little GTI's. Put those same cars in the hands of someone who can drive really well and you'll never see them on the track.
That being said, what is your ultimate goal with this car? Just to do lapping days or would you like to get into some sanctioned racing like SCCA or NASA or AER etc?
For your budget, I'd recommend you get yourself a tow vehicle and purchase a used race car. You'll save a TON of money buying a used race car rather than building it from scratch. Most of the great track/race cars can be found used (
www.racingjunk.com). REMEBER: No matter who built the car, it's all about the maintenance and upkeep by the current owner that makes the difference. If Bimmerworld built a 330 and it's been neglected for the last five years by its current owner, it won't necessarily be a good buy.
A fantastic race car is a Spec E46. They punch way above their weight with a fantastic suspension and maintenance is relatively low since it's an E46 330. They are very predicable and easy to handle. They're also pretty light weight and you can find very well built cars for in the low to upper $30's. You can find various well built BMWs (E36 and E46) for less than $35K too.
A spec E36 would probably be a bit boring for you. They are SO easy to drive and a fun/cheap car to run, but just a bit gutless and slow compared to an E46.
I've spent the vast majority of my racing time in a 2008 335i. It has a Dinan tune so it makes about 400hp, but no aero or real weight savings (3,300lbs). It's great on bigger tracks, but difficult to keep up with the lighter cars with aero through the turns. We usually run endurance races in either SCCA or AER.
Spec Miata is a VERY good car to learn and pretty cheap to run as well. It's more about the competition amongst themselves rather than all out racing. They can be pretty quick (newer build and setup correctly), but I'm not sure if that's what you're looking for based on your first post.
P-car tax is pretty steep when it comes to running costs. Yes, Porsche has "fixed" the issue with IMS, but you can run into bore scoring and it an engine does let go, you're in for at least $10 - $15K for a replacement. Plus the consumables are pretty expensive too. I know plenty of guys running Porsches and they do spend quite a bit more than we do on the 335.
In the end, If I were you, I'd get a dedicated track car ($30K), enclosed trailer ($10K) and tow vehicle ($20K) and have money left over for some real fun. It's the best way to have fun on the track without having to worry about wrecking your daily driver or fun street car.