A ten gallon is great for a betta! The more room the better! But you'll need a filter and heater. And you'll need to set the tank up and allow it to cycle for a while before adding your fish.
There are plenty of options for an algae eater. Your probably thinking about a pleco. Most species of plecos can grow to be 18 plus inches. I believe the rubber nose stays at like 5-6 inches, and same with the clown pleco. But I think your best option in your ten gallon would be Oto, they are super cute and stay really small. You could get 4-5 of these. Mystery snails are great additions to your tank too. And any kind of shrimp, I like the japanese algae eating shrimp, a bit more expensive but well worth it. Then you have the perfect clean up crew.
Heres a little oto