I also want to welcome you here! You'll find that quite a few of us are willing to provide assistance, and Cory is definitely one such individual!
His statement about MacKeeper is certainly accurate, and it needs to be avoided like the plague.
Regarding your questions, it would be beneficial if you could let us know 1) what version of the Mac OS X are you using (the latest is Yosemite, V10.10.3), and 2) what exact Mac model you have. For now, I can try and provide some thoughts/ideas, etc.
First off, it is best to get into the practice of doing as much self-cleaning as you can. If you no longer need something, then get rid of it. This includes unnecessary EMails. (By the way, when one deletes an EMail, it does not go away completely. I use Outlook, and that is the case. But, there is a way to permanently remove deleted EMails in Outlook that I use. Quite a few folks around here use Apple's Mail program, and I believe the situation is similar).
Secondly, whenever one installs an application, the installation actually includes a number of associated files. A good, free program to use for completely removing an application is "AppCleaner". You can get it from here:
http://www.macupdate.com/app/mac/25276/appcleaner
Third, for some more, safe cleaning of stuff, there is the venerable free program entitled Onyx. That one has been around for quite a long time, and has had numerous positive reviews. For myself, I rely on it as part of my arsenal for performing disk maintenance/repairs/backup processing. You can get that program from here:
http://www.macupdate.com/app/mac/11582/onyx
Note, though, that the version you need depends upon which version of OS X you are using. (Note the "Related Links" part of that link).
Fourth, for performing disk maintenance/repairs, there is Apple's free Disk Utility program. However, there are times where it would be beneficial to have a more robust program such as Disk Warrior or TechTool Pro for such tasks (and more). I have both of them, and again (just like Onyx), I rely on TechTool Pro.
Finally, it is mandatory that one do backups. There have been numerous times where folks come here for assistance, but do not have a backup. They are not that difficult to perform. The "type" of backup you want to use depends upon your needs. Myself, I use the excellent backup/cloning program called SuperDuper! to perform my weekly backups for each of my machines. The advantage of such a program (Carbon Copy Cloner is another excellent choice) is that it creates a
bootable backup of your system
at the time you did the backup. For some folks, that is not often enough, and they use Apple's free Time Machine to perform scheduled backups of files and folders. However, Time Machine does not create a bootable backup, so recovery could be difficult, depending on how/what you need to recover. With a backup that SuperDuper! creates, one can just boot to that backup, and then perform maintenance on the original machine/disk, and do a complete restore, thus being back in business quickly. There is a "free" version of SuperDuper!, although it runs somewhat slower than the paid version (only costs $27.95). The paid version allows one to schedule incremental backups, similar to Time Machine. I have the paid version, but have never used (nor needed to use) that feature. I can tell you from direct experience that having such a bootable backup saved my "bacon" twice with my Mac Mini.
You should read through this thread about backups:
https://www.mac-help.com/threads/backup-your-mac.211710/
