[CREDIT] Which credit card should I apply for?

I am 25 years old. My credit score is around 680. I currently have a $3,000 limit on a credit card that I have, but due to some private family business I'll need to close this account, and open a new one.

I want to continue building my credit, and pride myself on being good at personal finance. I keep my credit utilization low, and have been complimented on my credit the 2 or 3 times I have had my credit checked renting an apartment and buying furniture. I've never carried a balance, and I've never paid interested.

So what is a good option? I know a little bit about rewards and points, but I'm not overly concerned with them. I'd prefer a card with $3,000-$5,000 limit, but not sure if that is possible where I'm at or which card to apply for...