There’s nothing wrong with riding an older bike. A couple weeks ago I bought a mint 1995 GiantInnova hybrid with a few accessories and absolutely love it. With the adjustments/modifications planned, Iwill still only be about 30% of what a new hybrid costs. Keep and rock that old bike!
As far as tires goes, I have used the Michelin City tires on my old MTB. They are 26x1.4 and ride very nice. They max out at 87psi so they have verylittle rolling resistance; yet, they still feel strong enough to ride hardpacked paths. For bringing an old bikeback to life, they are good tires to roll around on.
Good luck with the old Giant. Post a picture or two if you have any.