I just picked this up and am looking for ideas on a very tight budget build?

COOL!! I just picked up a 48 Dodge 3 window coupe. I'm trying to figure out the same thing.

1st question (to both guys), do they run?
Can they be made to run?
Would you want to drive the flathead 6?

What I do with all these 40s & 50s Mopars:
Fix the floors and rockers.
Install a disc brake conversion, a modern master cylinder (on the firewall) and a modern rear axle. It really is cheaper then repairing the existing brakes and when your done, you have better brakes.
If the flat head runs, I'd consider driving it, they really were not bad with 3:23 rear gears or a 3:55 with an OD. They will run 70 mph all day.
If the flat head is dead, I would install a modern motor and transmission of your choice. For me it would have to be Mopar, and they fit as good as any other motor.
Fix or replace the seat, add seat belts, and drive it. Gene

New bushings in the stock front suspension, new shocks, disk brakes.
Different rear end, like a 3.23.
318 904 combo, really I'd prefer an A998 or A999 with the deeper first gear but they all look like a 904 anyway.
4-barrel on the 318, 360 cam, 360 or Mag exhaust manifolds or block hugger headers.

Decent tunes

Cheap seat covers.

Go Go Go. Put some miles on it.

Learn to deal with the admiration. If my '64Dog attracts attention and approval, that thing will be on fire!

R.

First thing I would do is address the rust situation.

Maybe This:

All great ideas! Thanks for the input

4" CHOP!!!!!!

Volare,mirada,cordoba transverse torsion bar front suspensions are a easy cheap swap comes out as one piece notch your frame to sit on k member with proper caster and weld it on instant power brakes,steering and adjustable ride height.

b body rear axel fits well, add mopar engine of choice 383 or 400 cheap reliable power small block fine also

A freind of mine has one with a five inch chop 440 powered has been flat black far before it was cool bad looking car...

great find!!