The first thing to do is measure your rear dropout spacing... Older 7-speed bikes generally used 126mm dropouts. Newer 9- and 10-speed hubs require 130 mm spacing. So tou will likely need to "cold-set" (i.e. bend) the rear triangle to fit the larger hubs. That is probably best left to somebody that has some significant shop smarts.

You may find it easier/better to change the front chain wheels instead. What are you running in front?

Use one of the many online gear calculators to get a feel for how changing front and rear tooth counts affects overall gear ratios and rideability. Google is your friend!