Hi Alex! Congrats on being in a solid financial position, that is awesome. I invest out-of-state but I initially started buying "in my own backyard." Personally, I'd be nervous to buy out-of-state for my first rental. I've found that those 20K-40K properties aren't as cheap as they sound at the end of the day because of major repairs/rehab work, closing costs and high eviction rates (common in some of the lower-cost markets where you'd find these cheap properties). But buying out of state definitely can work if you do your research and have help from a knowledgeable team.
I started out with a house-hacked duplex in my city, which was perfect--I was able to live onsite and get some experience as a landlord while minimizing my expenses, dealing with the quirks of being a first-time home owner and offsetting the costs of my mortgage by having renters. That experience gave me the confidence to keep growing.
With 10K in savings, an attainable goal might be to get an FHA loan on a single-family home and still house-hack by renting additional rooms to others (if you're comfortable with having roommates). One of my clients started out by doing that and will soon be buying his second property. It's worked pretty well for him.
Good luck! I hope this is helpful.