Getting Pre-approved before making rapid offers. Details?

[Garrett Ellison]

I've got some funds secured for buying my first rental property!  However, I have a couple of newbie questions.  I feel like some of these small details get left out in the podcasts.

I'm assuming I should get pre-approved before I start making offers.  How did y'all most easily complete this step?  I've also heard that you should only get your pre-approval letter for the exact amount that you're offering, otherwise the seller will assume you could raise your offer.

How did y'all complete this step?  Form a relationship with a local credit union and get them to write a different letter for each offer? Or just get a pre-approval letter for as high as your niche budget is?

Thanks!