Great questions guys. I'll try to shed some light. I'm a Mortgage Broker first off, not a bank. So why I say is from my side of the field. I am the Broker for my company and not just a Loan Officer.
1st, 5th 3rd and 3rd Federal are both good places to look. But, know what you are looking at with them. The only have their programs and they are a little strict. They tend to work with people who only have good credit. That's not the case for everyone wanting to own a home. The rates have some variance, but both bank have average rates for banks. Brokers have access to lower rates, for the most part. The reason is, Brokers get the whole sale rate. Banks work with retail rate and restrictive programs.
2nd, "get a fixed rate". It depends on your position. If you are planning on staying in the home for a while, than yes, a fixed rate id the safe way to go. If it's a starter home and you know you are going into some thing else in 5 years, look into the other programs that are out there. It doesn't mean you have to go with them, but at least be aware of your options.
3rd, First Time Home Buyer programs. There are several. KNOW WHAT YOU ARE GETTING INTO. Some will put $ up for you. Some require you not exceed a maximum income and my require you prove you have not made too much or they with raise your rate. For the most part FTHB programs work. But, Many Lenders(not banks) have programs the don't require money down other than closing cost. Fixed rates can be had regardless of the amount of money you put down, or none at all.
4th, Prepayment penalties. What is a prepay? It says if you refinance your home with in a given time (Most prepays are 3 -5 years, some are shorter) you have to pay a fee. The law just changed on this and I'll answer questions on that one on one. Again, know what you are getting into. A prepay and be helpful. How? If the lender is offering a lower rate with a prepay of 3 years, and you know you are not going to be in a position to refinance in that time, why not get the lower rate? If you sell your home the prepay does not apply.
I hope this has helped some of you.