The first thing credit card issuers look at when they consider your credit card application is your credit history. The pay limit is not that important, it is enough if you have stable sufficient income and permanent job.
Discover it® cards offer 1% cash back on all purchases and additional 5% cash back in categories that change throughout the year. The regular APRs for Discover it credit cards are the same (except the card for students), differs only 0% introductory periods. You may choose a card with the maximum 18 months 0% intro APR on balance transfers or a card with an equal 12 month 0% intro APR on purchases and balance transfers.
There are other benefits gathered in one Discover it card such as no late fees, no foreign transaction fees or pay your bill in last minute features. These features cannot usually be found in one credit card.
As for going for Discover, it would be better if you do not close your old credit card. Closing your old accounts you shorten your credit history which will negatively impact your credit score. If you are good in having more than two credit cards, there’s nothing wrong to apply for one more card.