We went with some friends running last year. Caught the bug and now have our project car.
"Low budget". Hmmm. I dunno. I thought medium budget and that is already pushing it. Lol
Take a look at the classes and results from last year. It's seriously competitive. Even street machine eliminator top 16 qualifying averaged I think 11.0x or less.
Depends on what low budget means to you and what skills you have. ;). And how dependable you can make it. A low budget strictly strip car is much different than one to drive 1k miles + in five days.
The Hot Rod category is cool. Less cars. Not as fast. (Remember all NHRA/IHRA rules).
Do you have anything to start with? Fox and F bodies are less costly to get into shape. You could take LS1 camaro/firebird, toss decent size turbo on it, roll cage, beef up rear and shed some weight. Or. Mustang.
I'd suggest going this year and tagging along. It's absolute blast and you can figure out first hand. People are awesome. You can follow along the route. Just book your hotels now. Lol
Hope this helped a little.