@Zachary Sexton, With regard to a mortgage broker, go with a local one (Austin has quite a number of great local mortgage companies) who will be responsive. Ask them straight up if they will respond evenings and weekends. I know a number of great ones who do. I also know a couple of loan officers who are investor. Stay away from the big banks, credit unions and national companies like Quicken. They may have great interest rates, but most will not respond when you need to make quick decisions or a custom pre-approval letter. I can provide some recommendations if you want.
Speaking personally, the issue for me is not how long you take to make the investment...it's how many properties you want to go look at before you make that decision. You can take as long as you want to decide to pull the trigger, but once you pull the trigger you should have narrowed it down to a handful of properties that meet your investment criteria. What most agents don't want to do is show you 20 to 30 properties...one at a time! It also helps for the agent to know what your definition of "right deal" is....that way you're more likely to find it. I want to know if you know what your criteria are...because it works both ways. Some investors don't really know what they are looking for, which makes it very difficult for either them or their agent to "know it when they see it."
I think finding out if the agent invests, or if he/she has worked with investors in the past. If so, what kind of investors....buy & hold, fix & flip, etc. Give them you goals and see if they have any suggestions. How familiar are they with rent rates, rental property requirements (Texas Property Code), doing background checks on tenants and writing leases, etc.
Hope this helps! If I can be of further assistance, please don't hesitate to reach out. Good luck!