I've been struggling to get a car together for years and just now am getting close. That's because I have went about it ALL the wrong way.
To make it short....I would try to buy a done car, at least a roller. I see cars on the internet that are selling for about 40 cents on the dollar (would be my guess). What a huge savings!! Not to mention precious TIME!
I would avoid any old, 1960's car that doesn't have a current chassis sticker on it. The old cars can have so much incorrect (diameters, placement, heights, etc.) that they can hardly be made to certify....cheaper, cleaner, safer to avoid the whole mess. (ask me how I know)
Also, be aware that different chassis inspectors don't always agree (especially true between different NHRA divisions). A car with a current or just expired sticker may not satisfy the next official that inspects it. Then it's back to the drawing board....weld, cut, etc. (ask me how I know).
If I were buying a car with any doubt, I would try to make the deal contingent on the car passing chassis inspection in my home division....even if I had to pay for the recertification myself. (yes, ask me how I know).
If you get a car that won't sticker you will be lucky to get a sand-dragger to take it off your hands. (sadly, ask me how I know).
Finally, I developed the habit of getting on ebay or the drag cites (or going to a swap meet) and buying junk with no real plan (regarding the part). Yea, got lots of cool old stuff but, geez, what a waste of money.
SO, there's all the brainless mistakes I've made.
If money and time are an issue (when isn't it?) Have you though about a partnership? I know a couple guys that split the cost and get twice as much work done.....one weekend John Doe drives and the other crews / next weekend Joe Blow drives, etc. They have a lot of fun.
What about making an offer on a hometown car? ...one that you know and the track officials know? Racers are often dreaming of that next project, higher class, lower ET.....might just get a handshake. Since you're new, the old owner may be very friendly to the idea of coaching and helping you with his old car.
Well, anyway, please avoid the dumb things I've done and good luck.