It's this old house, not this built after your dad was born house.
See if you can find a dented water heater - their outer shells get dented but the inside tank is undamaged - and they go for less. Plumbing supply houses sometimes have them. I replace about 20 water heaters a year, and I always pick up dented WHs at a discount. Sometimes folks don't like them, so they get undented ones at full price.
Re-pipe is another issue: much more involved and more expensive than a water heater. But don't let your galvanized pipes eat up your new water heater.
Are you going to do this yourself? I know this won't be welcome news for someone in a tight financial situation, but sometimes even the simplest plumbing jobs turn into a can of worms. One issue will run into is that your existing pipe fittings won't mate up to a new water heater. New water heaters have "heat traps" built into the inlet and outlet fittings, and they are usually the reverse gender. They will be male fittings and your old water heater may have female fittings.
That means that at least a section of pipes next to the water heater will also have to be replaced. If your current water heater is in good shape, you might see if it is possible to replace the inlet tube only. This is only economical if you DIY, otherwise the labor alone is too high to justify this approach.
BTW, you didn't say whether you are on a well or not. A new water heater will not solve the problem of being on a well, that is something you have to learn to live with. I'm on a well myself.
We're here to help, not bash anyone. But we're people with personalities too so please bear with us
Your galvanized pipes do need to go, as does your old WH, but if you're on a well I suspect water pressure variations are the biggest culprit in the temp variations. You need two people with direct communications (cell phones) to determine this- one at the well and one at the tub. If the variation coincides with thew pump running then you need to check the well pressure tank to be sure the bladder is OK and that it has the correct volume and pressure of air in it. Even in a good system air migrates through the bladder so it needs to be pumped up every few years. Failure to do this results in a torn bladder and a new pressure tank- in fact this is the most common well problem after water quality.
Dealing with old plumbing can be opening a can of worms, especially with old galvanized pipes, so I'd want someone with finesse and extra parts on had doing the work. It's all too easy to break old galvanized piping and as fate will have it, this will happen in an inaccessible spot or in a wall somewhere. If you must replace the WH I would see if it were possible to replace it's plumbing as far as is easily accessible. Later on when funds recover you'll be that far ahead with replacing the rest of the galvanized. Habitat Re-Stores sometimes have new WH's but it's hit and miss there. They will probably be damaged in some way but it's often just cosmetic though you do need to check carefully as they don't do refunds. Same for Craigslist where a nearly-new one may surface.
Unless you're confident working with old galvanized plumbing and working with gas lines, this is not a DIY project.