I'm no expert but just finished two bathrooms, and since you have access to all of the plumbing and want to replace that anyway, why not just cut out the old pipes and replace everything with new?
Since it looks like you're dealing with galvanized, if you replace with that, for a first time plumbing job it might not be that bad, though if you look around on the forums, you're sure to find advice and tips for soldering copper pipe or other alternatives.
It feels so good to rip out the old plumbing, and in my case, the 50 year old galvanized was so gunked up inside, switching over to copper and undoing some of the really poor work that the previous homeowner did felt really good.
I went with Delta shower/tub faucets and found the installation pretty straightforward.
I wish you the best. Test out all of your work before putting the wall back up for a bit of peace of mind.