Well, this is the worst possible time to buy a home. My advice is to wait. Save, save, save and wait. You should have 20% down and be able to comfortably afford to make the payments on a 15 year fixed interest loan. If you can’t do that, you likely can’t afford the house. Adjust your expectations accordingly. If you take a 30 year loan plan on making the extra payments like it is a 15 year loan. If you’re not disciplined enough to do that take a 15. Do not get a 30+ year term loan, don’t. It’s a rip off. First time buyer rates don’t really exist anymore and try to get your loan from a credit union and not a mortgage broker. Get a conventional loan. Zero down, 80/15/5 loans or any mention of a “balloon” run away. Do not get an adjustable rate mortgage. It’s also generally a rip off.
As far as your rate is concerned, shop around and keep your credit score up. Not much more you can do.