I rewired my 53, at least the engine, overdrive and headlights so far. pretty inexpensive if you do it yourself. There are several methods. I tagged every wire at both ends as to where it connected, then removed the harness, stripped off the tape wrap covering, and cut each wire to match the old ones in length and color.
Here's a link to an earlier thread on rewiring:
http://www430.pair.com/p15d24/mopar_forum/showthread.php?t=13205&highlight=wiring
You would want either some basic soldering skills and materials such as heat shrink, or a good quality ratcheting crimper and plenty of decent quality end terminals. I like harbor freight but not for their electrical terminals. Too lightweight. Rhode Island wiring sells complete harnesses, great quality but up in the price range you mentioned.
Have you got a service manual yet? There is one available on ebay, under $30., called the 1946-1954 Plymouth Service manual. You'll need one and it contains wiring diagrams in addition to tons of other great info.
When I cleaned up the frame on mine when the engine was out, I first used a putty knife to scrape off 90% of the old goop, then plenty of Gunk foaming engine cleaner. A nasty job, careful you don't track it into your house. I did mine with the car over a tarp, and when I was done I rolled up the tarp and dumped it. Also threw away the shoes I was wearing.
It's a good practice to get the car running, charging, etc. before the rework, so you're sure any glitches later are not due to your work.