Everybody has given you good advice. May I add a bit?
A tank the size of yours is going to be very difficult to cycle...it's hard to hold a cycle even a 5 gallon(is that about 20L?) tank. But it is possible to keep the tank clean enough for Tony, I have seen doing one 50% water change and one 100% change per week. You would take him out, preferably in a cup you can cover, and do the big change in his tank. If you can't get catappa leaves, I have used oak leaves with good success...but my guess is that once you give him some surface cover, he won't really need the catappa anyway. As far as floating plants go, you can leave many things floating, such as anacharis, hornwort, and even java ferns and anubias don't necessarily mind.
You are doing great by improving things for Tony! He will reward you by being happy and spritely for you once you've got the routine down and he's continually in a clean, safe environment. Chances are good that he's suffered a lot as a pet store betta, and he has to heal and get used to humane treatment, just as you have to learn how to provide it. You learn together (not to sound too hippie).
1 - 55 gallon planted community
3 - 10 to 20 gallon planted betta tanks
My advice: slow down, think, and be willing to learn. Then you'll be fine, no matter what.