Just off the top of my head.. Capital one Venture, Merrill Lynch plus, Navy Federal , Chase Sapphire and possibly Penfed.
Also, would you recommend requesting Credit Limit Increases first or Applying for some new cards first? I think I read somewhere here that Capital one does a soft pull for CLI, so maybe I should do that first? and should I request a CLI on my Cap 1 with $300 limit or just close that sucker? or will they combine with my other Cap 1? so many questions...I know I know! 
Yes...for sure, do your soft pull CLI request first. BofA will be a hard pull on TU for CLI. Check your account for the blue text "increase credit limit". If you're looking for a new card with growth potential with BofA. I'd go ahead and App for that card(Merrill Lynch plus). BofA will pull EX and use the same pull in most cases for the CLI request. Shoot high when requesting a CLI with BofA. If it is an instant for your asking amount. You've left money on the table. If they counter offer. You've hit the ceiling till another 90 days passes and you can try again.
I picked these banks and CUs because they're known to be generous. Chase, BofA along with a few other large national banks normally use a computer to give you an instant decision. Some want a banking relationship in order to give you a card.
IME those that have instant decisions, give the highest SLs on average. Verses lenders that do manual reviews . Penfed and Navy sometimes will manually review apps. There's really no way to know if their systems will approve you instantly. I'd say there's more of a chance Navy will approve instantly vs Penfed.
You also can research what credit report each lender pulls(google credit pull data base) And use that to your advantage. Some lenders are more adverse to new accounts than others. From what you've said so far. You shouldn't have that issue.
You can't be afraid of being denied. It will happen sooner or later. Don't let that discourage you. If you're getting denied back to back. Time to take a break and allow your reports to cool off.
Try to find cards that will be useful in your household as well. That means doing a lot of research.
Ok, so I CLI'd online on my Cap 1 card (current limit $4400) and got the 10 day message:
"One of our credit line specialists is reveiwing your account. You'll receive the results of our reveiw in approximately 10 days."
Wondering if I should still CLI on my other Cap 1 ($300 limit) or wait? 
It's been a while since I got a CLI on Capitol one. It was every 90 days when I was doing it. That's been over a year ago. Thought I read it's every 6 months now.. though I could be mistaken.
Shoot for the stars with BofA! They'll counter offer you, if you shoot too high. $20k is a good one.
I wouldn't be surprised if your BofA doubled in limit.
Penfed is a good one for Auto loans. You can use the same HP for their other products as well. It's a HP on EQ to join. So you might as we'll get it all in that HP.
Yes your scores may dip a little after the loan reports. They'll rebound quickly. In two months or so, your scores could possibly be higher than before adding the auto loan.
If you don't have an installment loan. No doubt, it will help you in the long run.
App for Merrill first then do the CLI request. They'll pull EX. If you do it the other way around, they'll pull TU for CLI. Not sure if they'll use it for the Merrill Lynch app.
With income, there's no magic number. I've used my income on certain apps and household on others. I input $100k household or less for individual income.