Some features to be aware of are:
- Annual fee (or lack thereof)
- Payment network (Visa/MasterCard/American Express/Discover/etc.)
- Cash back/rewards rate (i.e., how much cash/rewards points you get per dollar charged)
- Interest rate
- Foreign transaction fee
- Extra benefits (e.g., free FICO score, "purchase protection" where you can get a refund in certain circumstances, etc.)
- Credit score requirements (i.e., how good your credit must be to obtain the card)
How you prioritize these features will depend on your specific circumstances. For instance, if your credit score is poor, you may have to choose among cards you can get with that score, and not have much choice on other dimensions. If you frequently travel abroad, a low or zero foreign transaction fee may be important; if you never do, it probably doesn't matter. If you always pay the balance in full, interest rate is less important than it is if you carry a balance. If you frequently travel by air, an airline card may be useful to you; if you don't, you may prefer some other kind of rewards, or cash back.
Cards differ along numerous dimensions, especially in the "extra benefits" area, which is often the most difficult area to assess, because in many cases you can't get a full description of these extra benefits until after you get the card. A lot of the choice depends on your personal preferences (e.g., whether you want airline miles, rewards points of some sort, or cash back). Lower fees and interest rates are always better, but it's up to you to decide if a higher fee of some sort outweighs the accompanying benefits (e.g., a better rewards rate). A useful site for finding good offers is NerdWallet.