Lenman, have a look at the following article about upgrades of older iPhones.
What you need to know about iOS updates
I also suggest a backup then clean install. Its a pain, but if this is the first time since new, your 6+ has probably accumulated a lot of crap.
There are a lot of sites that give advice on how to improve iPhone performance. I found that restricting background processing only to those apps that really need it made a big improvement for me. Deleting the Facebook app and accessing Facebook via Safari also helped a lot.