The limit you indicate is generally available to people with limited (or average) credit history, in other words, students or young people earning their living. To qualify for $2,500-$3,000 limit credit cards, a person should have a valid credit score available with one or all the credit bureaus and should have no bad payment records with any previous or current financial institutions.
If you comply with these requirements, you can choose from among credit cards issued by Capital One Bank, a major provider catering for customers with limited credit history.
In case you're a young adult, owning a stable income and permanent job, you can consider applying for Capital One Standard Platinum, a no annual fee card for average credit, or No Hassle CashSM Rewards, a low APR Capital One card with cash back rewards.
Both cards will offer you up to $3,000 credit limit if you qualify.
Are you a student with a full time job? Then take a look at Standard Platinum for Young Adults credit card from Capital One Bank. This no annual fee credit card for limited credit will not only give you the funds needed but will also help you build credit if you follow the basic rules of good credit management.
So, make sure you have no bad credit records or inaccuracies in your credit report, you have a valid credit score and a stable income and then apply for a credit card best meeting your requirements.