Dude! I'm in SoCal area also. What part? You should come by our shop and say hi. Were located in Northridge near the University.
I would highly recommend buying a car that is already track ready and has a logbook. I also used to think that building a car would be cheaper and faster than buying a race car that has been raced previously. Boy was I mistaken. It took 3 of us a year to get it on the track, and that was just for HPDE. We spent another year getting it race ready with mirrors, radios, cool suit, safety gear and tuning. If your going alone, you can easily spend 2-3 years building a car from the ground up, and you will be killing yourself financially. The time commitment isn't worth it! Even for all the fun your gonna have doing it. By the time your done building, you've gone through all your money and the cost of safety equipment and race fees is a larger burden than before. Just buy your first car, trust me. Build another one later after your connected, it will be much easier and cheaper once you have some friends in the biz. Sometimes you just get free parts for trade or because your in the right place in the right time. Somebody is way more likely to help you out when they know they'll be seeing you the next race weekend and your battle can continue.
BUT... If you decide to build you car, don't worry about the engine power too much. There is a little bit of gains to be made in the engine, but you can go years into the sport without even touching it. Just make sure the compression is good, put the timing to 14-16 BTDC and have at it.
Take the extra money you save from leaving the engine alone and buy an AIM SOLO lap timer. This little tool is worth more laptime than any performance part allowed by the rules, maybe even 10x more performance. Its literally the best bang for your buck you can get, if you are just getting into racing, its almost more important than fresh tires. Buy it before you go to HPDE, put it in your 240. Learning how to drive a Miata fast is the whole point of Spec Miata. The cars are basically dead even so you can make up 2-5 seconds just by driving well. I've seen a guy do it in a day. Not a single change to the car. The $2000 the top runners spend on their cylinder head is maybe worth 1 second. FORGET IT! Just get out there and start driving ASAP. Racing isn't about the car, its about racing.
In Spec Miata, the cars arn't fast. And even if they were, they're all the same so its not the car that is fast its the DRIVER.