I'd use something like CreditKarma to get an idea of what your score is likely to be, then call a bunch of lenders on the same day and ask them what their rate at par (meaning no points buydown) is for a credit score of <insert your score here> and a down payment of <insert your downpayment percentage here>. Since rates go up and down daily (sometimes even morning and afternoon nowadays), you'll want to call (or check online) at the same time so you're comparing apples to apples. After doing this a few times, you'll get a feel for who is the most competitive on rates pretty quickly.
You might also get a sense of how easy it would be to work with the mortgage company. A lower rate is fantastic but you'll probably have a mortgage for a few years, and them doing everything accurately and properly is worth something.
For now you just need to get a sense of the top few companies that you want to work with. No need to start an actual loan application or anything (which you can't do anyway - one of the things on the loan application will be the address of the property you're buying, a data point you obviously don't have).
Note that many lenders will compete on rate and then make it up on fees, so you are actually probably better served for asking their APY (which is supposed to incorporate the fees). The APY will be higher than the APR; the larger the difference between the two means the larger fees. You don't really care much; the APY is probably as close to a true price as you can get without getting really into super-nitty-gritty details (which you're not ready for).
When you've found the house, make the offer and start the loan process with your top candidate. When you really start, they ask you to put down a deposit of some sort to discourage you from starting the loan process with your top three. If you continue and get the loan with them then they'll credit the deposit to you at closing; if you switch you'll lose the deposit. IIRC the deposit was about $500 when I did my last loan about 10 years ago, but things vary by market and company.
I didn't choose my current home based on distance from work, but it ended up being about 15-20 minutes from my final job. I liked that amount of commute - not too long, not too short. If I lived right next to work, I don't think I would have liked it as much (also the area around my final jobsite wasn't really a residential area).
Sometimes you can be clever or contrarian and find places that are not far away in time but may be far away in distance. Around here, suburbs right off freeway exits are popular. At one point I lived closer into town and worked further out, and that was nice because I was commuting the "wrong" way and had very little traffic issues.
Honestly what I did was put together a big spreadsheet and list all of the factors that were important to me and then give points to each house I was considering, weighting the points by how important each factor was. Then I looked at the house or two that were the top point-getters. Basically a Kepner-Tregoe decision analysis, although I hadn't learned that technique at the time. Sure enough, the top point-getter was also the one that I subjectively liked the most, and it's the one I now own.
Point for you being that it's pretty specific to each person what their factors are, and closeness to work is only one factor (albeit one that MMM seems to emphasize). Lots of other things come into play.
Good luck.