@Megan Greathouse, I am up in Duluth MN and most all homes have basements. I am new to the REI portion so I can't speak on effects of having or not having a basement on rent-ability, but I can speak to the construction aspect.
From a construction side, my understanding is basements are used in colder climates where you need to get below the frost line to avoid heaving of your foundation. So by digging a basement (rather than just a foundation since you will be digging anyway) you are getting below the frost line and gaining more usable space for the home. Up in MN our frost line is around 6', but a quick Google search determined MO is closer to 2'; so that would make sense to not see basements on all houses like we do up in our colder climates.
As far as investing in a property without a basement, I would just be sure that if the properties you are looking at have a suitable foundation/ footing depth compared to your frost depth to avoid any expensive foundation issues. I hope this was somewhat helpful.
Thank you and good luck!
- Sam Torvinen