It’s not a good idea to uninstall 1.8.6 if it’s in /usr/bin. That is owned by the OS and is expected to be there.
If you put /usr/local/bin in your PATH before /usr/bin then things you have installed in /usr/local/bin will be found before any with the same name in /usr/bin, effectively overwriting or updating them, without actually doing so. You can still reach them by explicitly using /usr/bin in your #! interpreter invocation line at the top of your code.
@Anurag recommended using RVM, which I’ll second. I use it to manage 1.8.7 and 1.9.1 in addition to the OS’s 1.8.6.