A couple tips to keep your account safe post-purchase:
1) Change the account password, and link it to a new email that hasn't any other acc linked to it.
2) Change your account name before playing a game from the shop -> account (icon on the right side) -> summoner name change
3) Change your riot id to a new one by following this link, then type in a new riot id and tagline then submit it
4) Before playing ranked games on your account you may want to play 10-20 Normal Games/Arams to clean up your recent client match history
5) Do not flame, avoid typing in chat most often. You want to avoiding having someone reporting you to riot support by opening a ticket. And for the same reason avoid opening tickets yourself.
My account has been banned. Can I get a replacement account?
Yes, there's a few conditions over this though. Accounts must not be banned for flame, scripting or such reasons. You must provide the current banned account details for me to be able to verify the account state, after verifying I will provide you with a replacement account.