How to do Clean Install of OSX but Keep iTunes and Photo libraries

Hi there,

Hoping someone can help me out with what I assume is a relatively straight forward process.

I have an iMac that I purchased in November of 2014. At the time, I was running a MacBook purchased in mid-2007. When I bought the new iMac, I used Migration Assistant to copy the entire contents of the old MacBook to the new machine. As you can imagine, there was a lot of rubbish that was copied over that had accumulated over the previous 7 years.

A year later, my still relatively new iMac feels sluggish compared to my girlfriend's Mac, which was purchased at the same time. I'm thinking that a clean install of OSX would do me good, but I want to make sure that I don't lose my most important files - that being my iTunes and Photos libraries (as well as various miscellaneous files, such as the contents of My Documents folder.

I have all of this backed up to an external HD using Time Machine. What I need to know is...

1) What is the easiest way to do a clean install of OSX?

2) Once the machine has been formatted and the fresh OS is installed, what is the easiest way to ensure that I can move my important files back on to the computer? Will I still be able to access the files that are stored on the Time Machine backup from the freshly installed OS, or will Time Machine see the fresh install as a new computer and not let me access them?

It's funny - I used to do clean wipes of my machine fairly regularly when I ran Windows a decade ago, but since moving to OSX, I never felt it was necessary. Here I am now with 10 years worth of data, much of which is rubbish and simply slowing things down, and I don't know how to do something as basic as do a clean wipe.

Hoping someone with a similar experience can help me out!

Thanks in advance.