That will not really be a ratrod by defininiton. A homemade car of no make or vintage is what your talking about & the licensing dept. will never let you do it in most states.
You want to start w/a titled car body. I suggest you get a 46-59 2dr of any available make that has good glass & no major dents. Cut the floor & firewall out & lift it up on camperjacks. Then get a modern car [70's or 80's]that has some structure to it [rather than just being a unibody shell] cut away all it takes to fit [use a tape to measure important things like wheel base, axle width, etc. before chosing a doner car] this modern 'chassis' up into the vintage body-shell. I did this w/a 54 Chevrolet and a 85 Amc eagle [yes I do have 4wheel drive! & 28 mpg]. I'm currently using it as my daily driver. It has cost less than $2000 so far including registration [which was no problem]plates, and liabilty insurance. I used only a reciprocating saw, angle grinder, tinsnips,jacks & other hand tools on my driveway...no shop, no lift, not even a oxytorch. You could use a welder to make it a very finished car or bolt it togather in case you want to change chassi later. Obviously there are a ton of details as to how to complete this operation & it would vary from project to project. I made up my "plans" as I went along. People ridiculed me, & said it wouldn't work. It was a lot of work, but it drives WAY better than most other rods I've seen people build. So yes it can be done on the very cheap.