When searching for a new credit card you have a couple options to take. You could apply with a small bank or a major credit card company. There are a couple factors you need to take into consideration before applying. Do some research and pick at least three different companies and choose from them first.
Do you have already have accounts like a car loan, mortgage, or checking account with a bank already? Then keep it all in the same house. This way it makes it easier to keep all of your finances with one bank instead of a bunch of different ones. Transferring money between accounts to pay bills is and view balances is much easier now. Calling customer service is much easier because now they have all of your info in front of them making it easier to answer your questions.
Most people have accounts with different banks already. Small banks will value you as a customer because they need you. The interest rates with their cards might be higher but you will probably be able to negotiate those because they need you as a client. They cannot afford to lose you. Customer service at a smaller company is usually better as they do not have to deal with as many clients as big banks.
If service does not matter to you and its options that you want then a large credit card company is your best bet. Some big banks have so many credit cards it might take you an hour to choose from all of them. You are bound to find at least one credit card that will fit your needs. The customer service might not be as good as a smaller bank but you can get what you want as they are competing against other large banks for your business.
Whatever route you take when applying with credit card companies, you need to make sure you do your home work. Do not rush into a credit card application without thinking if the rewards program or company you are working with is going to be able to take care of you into the future.