To get the cheapest credit card rate you might want to look for a fixed interest card rather than a variable interest card. Although the fixed interest rate may possibly be raised it is not the norm. Variable interest rate cards may start with low interest but if the central bank raises the base lending rate then your card issuer is likely to increase your interest rate.

You will be able to get a low rate if your credit score is good. Interest rates are increased for higher risk customers.

Currently, the Discover card is quoting interest rates of between 10.99% and 18.99%

Chase Platinum Visa card has a variable rate of between 14.24% and 18.24%

American Express Blue Card is between 12.24% and 19.24% depending on your application details and credit history.