I have Chase for checkings and a Freedom card; I like having them together (payments are always really fast, within 1 business day and having one login for two things is nice as well). I got checkings with a $200 offer and I got the money fairly quickly so it was worth it to me.
Quicksilver $10,000 | Better Balance Rewards $2000 | Sallie Mae $3500 | Freedom $3500
Why paranoid regarding checking + card with same issuer? Often there are bonuses for stacking accounts, and Chase is no exception to that.
Other than a serious hassle with a recent wire transfer which I've done like once in my life anyway, I've had nothing but excellent experiences with Chase though admittedly I don't have to talk to them much and they've been my cleariing house for all my income for the past 4 years.
