Yeah, Google Chrome is definitely speedy! I had been using Firefox for a number of years, but it was too slow. Opera is another good browser, not quite as fast as Chrome, but definitely good.
As for disk cleanup/maintenance/repairs, you can do some disk cleanup on your own, and on a daily basis. The "easiest" one is permanently removing EMails that you delete. I use Outlook 2016 for my EMail needs, and I need to press an additional key to have deleted EMails permanently removed. Not sure, though, about other EMail programs, nor how to do it.
Also, if you download any updates, you should get rid of the prior one/ones. Typically, such updates wind up in your downloads folder. Myself I move such updates to another location on my internal drive (SSD in my case), inside a folder entitled "Useful software". That way, I can easily keep track of all the updates I have.
As for software for doing the job, I use two products. One is the excellent, well reviewed, FREE, and solid program called Onyx. You can get it from here:
http://www.titanium.free.fr/onyx.html
Note that there is a specific version for each Mac OS, so in your case, you would download Version 3.2.2. I have been using it for so many years, and I depend on it. Its main features are cleaning our various stuff. But it also can Repair Permissions. Supposedly, ever since Apple released El Capitan, the Mac OS takes care of permissions. But, I don't buy it, as when I run the Repair Permissions feature of Onyx, it finds permissions which need repair.
The other product I use is TechTool Pro:
http://www.micromat.com/. That is another excellent, well reviewed program which has been around for a number of years. It has a number of useful features.
Besides my daily cleanup, once a week (usually on Saturday), I run Onyx and Tech Tool Pro for disk cleanup/maintenance/repairs, and SuperDuper! for my backups. I do this for both of my Macs, and I make two backups for each machine, to two separate external devices (SSDs). By doing that, I rarely, if ever, have issues. And both my Macs run fine, along with being "lean and mean".
One other thing that is important is to keep up to date on your software, especially any third party ones you are using. Some products have a "Check For Update" feature, and can download and install updates "automatically". However, I myself like to have the actual updater file/files myself, in case I need them.