Great Questions! I work for a community bank and I recently refinanced my mortgage on-line, so I can give you some insight to both worlds. I hat to throw a lot at you, but there is a lot to say on this topic.
To start, there are other options than your local banks. In addition to online lenders there are mortgage brokers, which you can find locally or on-line i.e. lending tree, and I would even throw in Credit Unions.
As far as the best place to go, I would heavily consider places referred to me if you don't have the time to shop around. You never know what you're going to get from place to place or even person to person. So start by asking friends and family in your area who they went through and what kind of experience they had. If you're using a real-estate agent, I am pretty sure they have to recommend three different banks if you ask. From what I have heard they will generally recommend banks that will consistently close on the loan the quickest from start to finish.
Local Banks - I believe most of these sources will be upfront with you regarding rates and fees. If you're shopping rates it will probably take time to compare multiple banks, although you may find some luck with them posting rates and fees on their website. You also have the comfort of being able to walk into a building and being able to deal with a person face to face for service. In general I think you will find that you'll be paying for this service via higher rates than you may be able to find elsewhere.
Online Lenders - If you haven't yet, check out my post on upfront mortgage lenders. I refinanced through one of these companies and was blown away by the service
I think with most online lenders you'd experience a lot of frustration with hidden fees, or higher rates than they lead you to believe you can get. I recommend checking out my post. There you can find a link where you can find a list of Cerified Upfront Lenders which give you all rate and fee information up front and they promise the deal will not change as applied for, as long as you qualify. Be prepared to have your mortgage immediately sold though, as many of these places don't specialize in servicing them. (I've been quite happy with the company mine was sold to.)
Mortgage Brokers and Online Mortgage Brokers - I have no personal experience with them. I have the perception that here is where you may find the most hassle with hidden fees, and not ending up with what you were originally expecting. Again, just my perception. Does anyone else have any experience with them?
Credit Unions - Again I don't have any personal experience here, but I think in general you'll find they may be a decent option. CU rates are usuaully decent, and I can't imagine they wouldn't be upfront about fees etc...
I personally feel the best place to ultimately end up if your planning to live in your home long term, is where you can find the lowest rate, assuming similar fees. I would certainly consider a national lender over a local bank for even a quarter point. That quarter point on $150k 30 year mortgage = $8,830 less in interest paid over the life of the loan. Is it worth $300/year to you for the local service? If you're thinking short term then you may want to find the lowest fees with a decent rate.
In order to complete an application be prepared to, provide verification of your last three years of income, i.e. tax returns, W-2's etc..., verification of assets, i.e. recent bank statements, possibly pay for an appraisal, authorize your credit to be pulled, among a few other things I can't think of at the moment.
You'll probably never find the "best" deal out there, so do your homework, find a place with a good overall deal that you're comfortable with, and run with it. It's a big decision so don't jump into anything too quickly.
If I think of anything else I'll let you know. If you have any specific questions as you're going through the process, post them here and we'd be happy to give our opinions and advice.