Personally I would try form the Chase Freedom. IMO one of the best rewards cards available and you should have no problem getting it, with a somewhat decent CL.
I would also suggest either Chase Freedom or Discover IT. You should be golden for both or either one. 
I'll definitely check out Chase Freedom!
We do like to travel, but I've never used a travel rewards card so I'm not sure how "worth it" they are - how quickly you can earn something legitimate, etc...if someone had a travel rewards card they loved with good benefits I'd definitely be interested!
I'm very happy with my gas/groceries card so I'm not looking for one of those; just something to round out my wallet a little.
Now here's the next question...whatever I decide to apply for, do I apply now, or wait a month, try for my Amex CLI and THEN apply?
OP,
Beyond the obvious choice of the Freedom, you could go about it a little differently if you're up for it:
Apply for the Chase Sapphire Preferred. Sweet 40k point signup bonus and decent extras that you don't get with the Freedom in terms of using the points in the Ultimate Rewards. However, even if that doesn't float your boat in the longer term, you could PC out of it and into the freedom later. While the rewards are not as attractive for day to day spending, the 40,000 point head start and waived AF for the first year along with some double point spending on restaurants and travel will likely outdo the Freedom's rewards over the first year by a considerable margin.
Consider: even if you somehow maxed out the Freedom's quarterly 5% spending (hard to do in lame quarters), the most 5% spending you can earn annually is $300 because it's capped at $1500 per quarter which gives you $75. The CSP starts you with 40k (worth at least $400) when you hit the spendign threshhold.
Then you PC before the AF hits if you don't want to keep it. Just a thought.
Start (Sept 2011): low-mid 600s. NOW: TU FICO: 801, EQ FICO 808, EX FICO 798 (PSECU). Goal: Achieved! Now Maintain!
I'd like to add either a Visa or MasterCard with decent perks (not everyone takes Amex, and I'm not comfortable linking some purchases directly to my bank account - sometimes a credit card is the way to go). Any favorites?
For reference, my AAoA is 5 years and my current scores are TU 826, EQ 701 and EXP 746. I opened the Amex last June; around the same time I took my first mortgage, and since then I've opened the CareCredit account for an unexpected vet bill. Received my 3x CLI on Amex in December; going for another 3x in June.
Hmm, are you sure your TU is 826, or was that a typo (or fako)?
Assuming you want cash back cards, I would suggest the Priceline Visa from barclays, the version that gives 2% back on everything (that version is at pricelinevisa.com). That's a good card for any purchase that you don't have a better card to use. And it usually pulls TU. The main problem is, I hear they really hate if you open other cards in the 6 months after you open their card. As in, they may just cancel your card if you do that.
Then either try for US Bank Cash+ if there is a US Bank in your area, and/or look into getting the various cards that have %5 rotating categories: Chase Freedom, Discover IT (which also has a good online shopping mall), Citi Dividend.
So, that's 5 possibilities, and each even has a signup bonus (except US Bank cash+).
