Updating water lines

Haha, that sounds like a plan!

Have owned several 3sty properties w/apartments, back in Philly.
"If it ain't broke, don't fix it !" is still good advice. Learning to do solder copper pipe is fairly easy, watch youtube, read how-to posts; fix any thing that needs fixing, but overall, I'd say leave existing copper plumbing alone. Deal with it if, as, and when, it needs work.
OTOH, if you have any galvanized drain lines, they are problems waiting to happen.

For your new bathroom, yes, run new 3/4" water pipe up from basement, for the simple reason that you will get better pressure in shower & sink.

CPVC is hands down the worst potable water piping available. It gets brittle with age and has no structural integrity under stress. Leave the copper until you do the remodel then spend that money more efficiently upgrading your piping as part of the overall plan. The only use CPVC has in our area is to run tpr valves out (as it should never get used). You actually will be de-valuing your structure by using that inferior product. But hey, it’s cheap and easy.(for a reason).

Change out the tub and shower faucet and see if that doesn't take care of your problem. Might not have to change as much
piping as you think. When installing your new faucet there are many different types of fittings that you can use
then you won't have to do any soldering. Good Luck....