Before you buy anything
A few things worth knowing first
Rent first, always. Almost every climbing gym rents shoes, harness, and belay device for $10-15 total. You need 2-3 sessions before you'll know what fit and features matter to you. Buying gear before you've touched a real wall is how you end up with a $90 shoe that fits wrong and never leaves the closet.
Get your belay certification before buying gear. Most gyms offer a belay class on the same day you pay — usually $30-50 including the entrance fee. Once certified, you can climb with a partner any time the gym is open. Skipping this means you can only use auto-belay walls, which cuts your route options in half.
Don't confuse sport climbing with bouldering. Bouldering is unroped, low problems (under 15 feet), no partner needed. Sport climbing is roped routes on tall walls, always with a belayer, and the gear is completely different. Try both in your first few gym sessions before you decide which one you want to pursue.