Hi Jason, as everyone else has said, welcome to the forum! You'll find a wealth of information here on the site and in Mark's book! Make sure that you check out the articles link above! Good stuff can be found there also!
From the photos, it looks like you have a lot of water damage! I'd pretty much plan on replacing the whole bathroom floor with new subfloor. The bedroom you may be able to piece in. Since you're on a budget, make sure that you spend your money on a good subfloor, a good shower piece, install shut offs, with a shut off panel. Then make sure that the flooring you use will protect your subfloor! I'd use something other than tile. Your best bet, and most inexpensive is sheet vinyl. Simple install for a bath, and protects everything!
Now, you mentioned those 'grey plumbing lines'. With the age of your home, I suspect that they might be the same plumbing lines that are a huge problem. I'd spend the rest of my money to have the plumbing lines replaced first. You'll also want to check and replace the insulation and your under belly before Winter hits! Once that was done, then concentrate on the pretty stuff in the bathroom.
There are plenty of places around that sell items at a discount. Check out a habitat for humanity store, if you live in a populated area. They are great for gently used items!
Basically, get the place structurally sound both in the living area and down under first. That includes repairing the plumbing lines, then move on to cleaning up the mold and repairing walls. If needed, take your time and use the other bathroom for a bit! We've all been there at one time or the other!
Last tip, if you get stuck, someone is always around here to help you out on the board!
Maureen
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Never discourage anyone...who continually makes progress, no matter how slow.
'Plato'