Help with backup and upgrade plan for old imac

I have an imac 2011 and I need some advice before I start overhauling the whole thing. Please don't give me grief about this but right now it's still running Lion. For years everything ran perfect until recently I started getting signs of problems- mostly my apps were quitting unexpectedly or freezing. Adobe apps, apple mail, you name it. I hadn't updated or installed anything new so I don't know why things changed. Also, the finder has some issues like will not find files in spotlight anymore. I'm not seeing total signs that the drive is failing, and usually a restart will get things working again. But something is surely wrong. I'm hoping I can fix whatever it is with some repair and OS upgrade. I bought a new external drive and tried making a time machine backup. The backup fails every time and says it can't copy files. I'm going to try reformatting that drive and trying again. If I can't get time machine to work, I may just try manually copying my user folder to another drive. At this point, I know I'm not going to want to go back to this old OS so I'm not sure what the point is of backing it all up. I plan to update my subscription based apps as well. Will saving the User folder allow me to migrate data from mail, iphoto, etc. to the new OS? After I get a backup, I plan to run disk utility to check everything. After that I want to install new memory and begin the update which has to go first to El Capitan. Not sure if I should just stop there or if there's any benefit for Sierra or High Sierra. Should I just do the normal upgrade process and hope for the best, or should I actually erase/clean install the new OS? Any advice on this is greatly appreciated.