Whatever you do, avoid Chase:rant: or BofA, or Wells, or any of the 'too big to fail' big boys.
But rather than go with a bank, big or little, I'd suggest joining a credit union. Higher interest on deposits, lower interest on loans, fewer fees, and all the services you'll ever need. They're insured every bit as well as the banks and, to my knowledge, none were involved in the recent bailouts.
I'm out in Oregon, but I imagine things are similar in the middle of the country. I still get free checking without having to jump through hoops. I can use virtually any other credit union's ATM for free. I can use the ATM in just about any 7-11 for free. I have full on-line access to my accounts. When I go in to a branch, I deal with folks who aren't trying to rip me off at every turn because Banks have customers, Credit Unions have members. I see there are several in the Lincoln area, do yourself a favor and check them out.