Know where your shut off valves are. Assume they don’t shut and locate the ones upstream from those and of course know where your main shut off is. Plumbing isn’t hard but often the work you need to do is in a cramped miserable space. It helps to have two wrenches. When cranking hard on a fitting it’s a good idea to keep the wrench on the next piece to prevent the torque from putting stress on piping further down the line. I hope this makes sense. You can replace old piping with PEX pipe and fittings. I don’t have experience with it but it seems easy. I learned to solder with a propane torch by practicing on a few fittings in a bench vice. Not hard but there are a few things you need to know. Metal drains are easy to replace with PVC. Good Luck
I doubt the spout pipe is soldered in, should be threaded. When cranking on pipes like that generally two pipe wrenches work best but if you can only have your hand on one side vice grips might work. You can try clamping it to a stud somehow lol. If it’s soldered though I’d think you’d need to cut it or heat the solder up with a torch to remove it but I’m betting it’s threaded. Don’t be surprised if it’s tough to turn. You might be able to loosen it up with a torch, be careful not to burn any wood. If you do have to cut it a pipe cutter or hacksaw will work if you have room. A reciprocating saw is an option.
I should mention I’m not a plumber though minor plumbing is part of my job plus I’ve owned two houses over a hundred years old. It’s hard to give specific advice remotely. You’ll figure it out. Adapt and overcome!