Spend as little as 10k and get something already built and you and your dad can go racing. (S13, R32, old school R31 etc)
Building a race car is hugely expensive. No build has ever stuck to budget and unfortunatley once you start, your commited lol
As Tocchi, if your on a small budget then drag racing isnt for you.
Maybe look at the MC series, or AEM Speed dome events and stuff like that. There are guys there racing standard type cars. The more hp you look for, the more chance it will go bang and start costing big.
Good luck