Credit cards come with a variety of interest rates, fees, introductory rates, penalty charges, and "bonus" items like cash back, insurance, or air miles. When you compare credit cards, you'll want to look closely at the ones that offer the biggest advantage in the area that's most important to you.
For instance, if you plan to carry a balance even for a few months on your new credit card, you'll want to look for cards that offer low ongoing interest rates. Some cards will advertise an introductory, or "teaser" rate, but after the introductory time period is over the default interest rate will take over. That rate may be quite high, but you won't know that unless you read the credit card agreement — which is something you should do before you decide if this is the card for you.
It's possible that your suited to a frequent flyer credit card earning air miles. If you'll be paying your card off every month, that may be true. Be warned that most credit cards with a rewards scheme such as cashback, frequent flyers or points will compensate with higher fees and interest rates. You may see a fee to obtain the credit card, an annual fee, and very high interest rates if you do not pay the card in full each month. Add up the charges and you're likely to find that the "free" air miles are actually pretty expensive.
Now you have established the features of greatest importance you can search for products that best meet your criteria using a financial comparison website. You can compare cards by class—for example, Rewards cards such as Frequent Flyer, Low Rate or Premium cards. Consider which card to apply for using this method. For instance, if this is your first credit card or you're early in your career with a beginning salary, a Standard or Classic card is probably your best idea. Many 'premium' cards, e.g. Gold, Platinum have stricter requirements for approval and may be aimed at high income earners. If you don't have a well established credit record, it is not likely you'll meet the requirements. If you apply for credit and are denied, your credit score will take a significant hit that will remain for several months.
However, if you charge quite a bit every month and pay the balance in full, a card that offers rewards like purchase insurance or cash back may be a better offer for you. If you do your homework and find a card with rewards you really want and will financially outweight any costs incurred then you could consider a rewards card. The key when comparing credit cards is to find the best credit card for you based on your planned use of the card, your credit history, and what "extras" you're looking for. Take your time comparing and selecting a card, and you'll have one that will fit your needs for a long time to come.