Most lenders will match or exceed the limits by a certain percentage, you're probably looking at $1000 - $2500 right now based on your existing lines. I can't imagine anyone going beyond that until you establish more experience with higher limits.
I think the Chase Freedom would be a good option. They may give you a high limit, but they can offer low limits instead of a flat out denial.
After you see how that goes, you can look at an amex revolver with a starting limit of $2,000. The 61 day cli will get you where you want to be.
I can only speak for myself here, but I had no problems with lenders exceeding my existing lines. I only had two $750 lines reporting, and Amex gave me a $6,000 limit on my Blue and Chase a $2500 limit on my Freedom. However, I had also had an Amex charge card for almost two years when I applied for both of those cards, that I had put just about all of my spending through. I'm sure that was influencing Amex more than my two CapOnes. Anyway, don't assume you'll have to put up with more low limits.
Your best bet would be trying to join a CU and applying for one of thier CCs. They are usually pretty flexable and your more involved with the application process, where your usually met with a CU rep and they help you along the way.
I currently belong to a credit union. I was thinking either trying at the CU or going with the Chase Freedom card. Thanks for all the info
Usually credit unions don't offer real great rewards.