Hi! I'm a realtor, but I'm also Mrs. Money Mustache, so I figured it was okay. :)
Note that you typically need a "pre-qualification" to make an offer, not a pre-approval. Maybe this depends on where you live, but here in Colorado, that's how it works.
A pre-qual, as we call it, is pretty easy to get and is based on what you SAY. A pre-approval requires all kinds of docs.
I would definitely look at multiple lenders for your pre-qualification letter before you make an offer. Once the offer is in, you won't have time to shop around, as you might be closing in 30 days and just getting approved, getting the appraisal ordered, etc. might take that long.
So yeah, pick your lender before you even go looking for a house. Have a pre-qual letter available in advance so you're not shopping for houses out of your price range. If houses in your area are going fast, you'll need that pre-qual letter anyway to make the offer.
Try going to your local bank, credit unions, etc. to find a lender. The lender I use works at a credit union and they have great rates.
I hope that helps!