Welcome to trial by fire! 😀

For the transaction logs, there's a lot to understand about the different recovery models. This site has a good stairway on the topic at http://www.sqlservercentral.com/stairway/73776/.

For the backups, I would not want to keep a single day's backup for each database and call it good. Look at writing a stored procedure to do your backups for you and schedule it in a database job. That way, you could generate the SQL to do the backup and include the date in the filename. If that seems a bit daunting, (which it should given the other work you have do do at this point) look at Ola Hallengren's maintenance scripts. They are free, very well-respected and maintained. The work's already been done. Anthony.Green included a link to the site it his signature. http://ola.hallengren.com/

My two cents. Welcome to your new position and good luck!