Heya, ideally you want him in something that is 2-5 gallons. You can get small glass tanks for under a tenner so doesn't cost a fortune. You can have a look about at the posts on current killers, there are quite a few about, including one in the pinned topics. Plants are a great addition to betta tanks, they love building bubble nests around them and hanging out in them. Try to get silk ones though, not plastic, as you don't want him to rip his fins.
His fins look a little tatty - quite usual for pet shop bought bettas. Someone with more knowledge than me on meds may be able to recommend something.