I give this advice a lot, but if you have a costco membership, go to their website, search mortgage, pick Veteran loans (in your case) and fill out the form.

Costco limits the max lender fees to $650 for "regular" members and $500 for "executive" members. They also do a pretty good job of making sure the companies on their list take care of their people. If you run into a problem with your mortgage broker, you can call up costco and they will help.

Honestly, even if you don't have a membership, it is worth thinking about. A 1 year membership is $55 (regular) or $110 (executive). When you compare that vs the 1% a lot of brokers will try to charge, you can come out way ahead.

Generally, the way I play it is to find one, maybe two to talk with, have them look over your financials and help you get a ballpark of what you can get approved for. Remember also, you will likely be able to get approved for more than you can afford. Make sure you think you can afford it, no matter what the bank says.

You should be able to get an idea of closing costs, down payment, how much you can get approved for, how much payments will be (don't forget to add in taxes and insurance if they don't), etc.

Once you are ready to go forward/have a contract on a house, give over your SSN and other info to multiple lenders/brokers, let them pull credit and ask for a GFE (Good Faith Estimate). While not set in stone, if they give you a GFE, in writing, it has to be reasonably close to what you would really pay in fees, get in rates, etc. Compare them and see who is best.

Don't trust anything they say verbally or even an off-hand email. If it is in a GFE form and is way off/a lie, it is pretty easy to get them in trouble, so they generally will be pretty accurate (as much as can be expected) on a GFE.