A single male betta is the perfect resident for a 10-gallon tank. Make sure the current is gentle and that he has proper heat and filtration. Include some plants, real or artificial, and some caves or decorations for him to hide in if he feels the need. You will have plenty of room to aquascape, and he will have lots of space for swimming. You can even have some critter tankmates such as an apple snail or some ghost shrimp if he is willing to tolerate them.
The other fish I would consider for a 10-gallon tank is a dwarf gourami. Like bettas they are anabantids, and they are very colorful. You may be tempted to get a pair for but I wouldn’t unless you are considering a larger tank. They can be aggressive toward each other, and a small tank doesn’t allow much space. However, if you wish to add a few more fish down the road, this may go more smoothly with a gourami than it would with a betta. (Personally, I would not add more fish to a 10-gallon betta tank.)
If you are willing to consider a larger tank, you have several more options. A green spotted puffer will need a 30-gallon tank (minimum) and brackish water, but they are great for single-specimen tanks. They do have some unique care requirements, so read up on them before purchasing.
For even bigger tanks, the oscar is a popular choice. These are large, aggressive new-world cichlids. You will need a least a 55-gallon tank, but bigger is better for these guys. Like the green spotted puffer, make sure you do your research before committing to keeping an oscar!