The 710 was a nice bike in its day and is as good as any reasonably priced production steel frame you could get today.

I'm curious as well. Why can't you use old chainrings with a 9/10 speed rear wheel?

Your existing shifters will only do 6 speed indexing. You can use them as friction shifters but for indexing those shifters are strictly 6 speed.

You might be able to adjust the derailleur just right and shift past the 6th gear and get it to work with 7 speed, but you're really better off with the correct shifter