Welcome to the forums.
How long have you had the 3 credit cards? (the store cards help a little, should not be ignored, but the CC are more central to your long-term plans)
What are the negatives holding your score down? Low 600's implies some sort of lates, charge offs, other derogatories. The timing of how long those remain on your file would be the clock that controls how your scores rise.
When was your last INQ and HP? The fading of that will have some influence.
Continue to make all payments on time, and keep utilization under control, and your scores will rise gradually, then jump and continue to increase after the baddies drop off.
Getting to 800 takes years, so your file needs to age with positives (and virtually no negatives) to get there.
Which CC do you have? Are they getting $500 to $1,000 approvals? Those are starter limits, not much of a positive, more of a starting point, basic credit. You need to let them age, stop apping for a while, build your file and then reconsider what you need to app for in about a year.
No more store cards. doesn't matter what store card, "approvals" or not, you've got too many 
and tell us about those negatives as well please.