Oh yes those dear transaction logs: can't live with them, can't live without them. Understanding how transaction logs work and how to manage them is the key to having a happy DBA life. The transaction log is basically a copy of all SQL statements run against your database, (except for things like bulk inserts in Bulk Logged mode, or inserts made when traceflag 610 is on). In a disaster on a database set on Full Recovery you can obtain a fully functioning database by first restoring the last complete backup, and then restoring any subsequent log backups. You may still of course have to manually run any bulk imports executed after the last dB backup, but that's seldom an issue.
The nice thing about logs is they backup really fast (they are after all just a bunch of SQL). I can back up a log for a day's worth of activity on a heavy production database in about 15 minutes. The nasty things about logs is they restore rather slowly (as the engine has to re-execute all that SQL). My 15 minute backup takes a good hour and a half to restore. The other nasty thing about log files is, if you go with Instant File Initialization and autogrow, then you need to manage their size by shrinking them. If the device hosting your log files for a database runs out of space, then that database won't execute any more transactions. No bueno.
Hence it's a good idea to add a customized alert to RedGate monitor when your log file expands beyond a certain size. Also I use a little trick to "flip" between different copies of the log file: right click on your database, choose properties, and then files. Add a couple files of type "log" but leave their size small and turn off autogrowth. Now when your primary log file gets too large, turn autogrowth on one of the small files, and off on your primary. After the next log backup you should be able to shrink the primary log file down to nearly nothing (well if there aren't long pending transactions still out there). In this manner you keep occasionally swapping between active log files as their size dictates.
Another nifty trick is to allocate an extra spare log file to a different physical device (but leave it small without growth). That way in an emergency where your disk drive hosting the logs fills up, you can just click into properties and turn autogrowth on your spare log file. Once that's done, backup and shrink the primary logs.
Of course if you don't want to hassle with the logs, don't need point-in-time recovery, and don't need them for log-shipping to a synchronized database, just leave your database on Simple recovery. You can then shrink the logs at your own leisure (usually after a full dB backup) and you won't have to worry about backing up the logs themselves.