Major banks are generally the same, and hold reputations similar to Chase. There are very few banks that have free checking anymore, I think 5/3rd and PNC Bank (student checking) offer these accounts. There are also a couple of major banks that offer student checking, where the minimum balance is lower than a regular checking account. It is usually $500 or direct deposit from your employer that will keep you from incurring any fees but things do change and it's best to sit down and talk to a personal banker if you have the time, and explain what you want and don't want. That being said major banks have changed in the recent years and try to up-sell everything they can. My advice, avoid the add-ons, if you just want a checking and can avoid opening a savings that you don't want, don't open it.
I've seen plenty of people get fees for accounts they don't know how to control. Start slow, you can always open other accounts later. Know the basic fees to avoid, like using other bank ATMs, writing too much checks, or doing more then 5(or was it 6?) online transfers from your savings account. All in all I haven't had any problems with Chase bank myself, but I only had it as a secondary account and never really used it. I've had Bank of America which I'd say has in my opinion the worst service and policies and currently have Wells Fargo, because I used to work there, but am not very fond of either. Just be careful and if do get an account with a financial institution anytime soon and mess up give customer service a call, ask for your money back politely (usually 1st timers get their money back) and don't commit the same mistake again. Good luck!