Hi Lori,
I've heard plenty of PayPal horror stories, too, but I've never had a single problem with it myself. I do get the occasional check, but I much prefer PayPal. It's immediate, easy, and lets me avoid having to take on the expense of accepting credit cards myself. I've heard complaints about the fees, too, but in my estimation they are far more than reasonable for the benefit you get in return.
You have several options for what type of system to use with PayPal. You can have the most basic set-up, using nothing but a bank account number and some contact info, or go whole-hog with online invoicing, automated payments, subscription plans, etc. Plenty of flexibility.
No, customers don't have to already have a PayPal account to use it. They just pick the option for "Send Money," fill in their credit card or bank info, enter your email address and amount, and click. It's done. (There is a 3-4 day approval delay for NEW customers who've never made a PayPal payment before, or returning customers who are using a new credit card for the first time, but after that, payments are instant.) You can also have it set up where your actual invoices bear a PayPal link and the customer only has to click without even filling in your address and amount, but that's an option, not a requirement. I just send my invoice and give my PayPal email address in the message. Simple enough.
For a "real" bank, I highly recommend BB&T if you have one in your area. Their
free business checking account has everything a small solo business needs and was a breeze to set up and use. Every time I've had a question, the staff has been fantastic. Online accessibility is available if you want it, no associated savings account is required (though you can have one if you want), and it comes with a debit card, so you can avoid going through the hassle and fees of a business credit card also. And it truly is FREE--no standard fees whatsoever unless penalties are required (overdrafts, etc.).
Have you gotten an EIN? If not, you may want to have your business account with a whole separate BANK from your personal one, not just a separate account, because some banks including BB&T use your EIN or social security number as your controlling identifier. I wanted to enable online banking for my business account only (which I intentionally keep "poor" because I'm convinced there's a thieving hacker around every corner). It is set up under my EIN. Had I set it up under my SSN, all of our personal accounts that bear my SSN would have become accessible online also. Not a big deal at all if you're not using online services, but something you might want to keep in mind if you do.
And by the way, I don't think a single one of your questions is stupid. Better to ask beforehand than to find out the hard way--and that's SMART.