Your car lease counts as an installment loan, so you're set there.
Applying for two or three cards in a short period isn't necessarily a bad thing, but it tends to work better if you have a thicker file with more history. People in a position to do that like the idea of seeing their new cards "age together."
I think Chase will accept you a few months down the road. They like to see a couple of cards under one's belt and at least a year of history. They're also sensitive to new accounts. And they'll deny you automatically if you have five new cards within the past two years.
If you'd like Chase cards in the near future, I'd wait six months to a year to apply. And I wouldn't apply for anything else in the meantime. If Chase isn't a priority, you can be more flexible.
32% utilization is a smidge high. 28.9% of your limits or lower is considered to be responsible borrowing. 8.9% optimizes your scores. With your scores being good but not excellent, I'd suggest going for the extra points first and applying when your utilization is 8.9% or below.
