It is likely either an issue with the charge port or the cable. Try the cable on a different device or buy a new cable to rule that out. If that does not do it, you most likely need to replace the charge port itself. This isn’t TOO complicated. If you are comfortable opening up the phone, you should be fine. If not, most repair shops can do this and it generally isn’t all that expensive. Just be careful with the home button as if you damage it, you cannot get touch ID to work again.
there are variations on each model so I cannot say what exactly the difference is, but overall the 910 is going to have a newer and better CPU as well as more ram from what I could find. The 910 would be much faster and it looks like the 760 is using processors that predate the core i series so at this point in time, I would say that if you are looking at buying either you should 100% go with the 910