Welcome to the forums olelady! (and by the way, middle age is not olelady... you still got a lot of life raring to go, especially if you are going for the adventure of an android, lol). I'm a middle-aged ole lady myself!
This is a tough one because there are so many out there. I think you should maybe start with certain features that you know you want and look at the phones with those features. That being said, I think you would be best to get a 4g LTE phone. I say that because Verizon is trying to get everyone on 4g to build their network and phase out 3g. Do you mind a phone with a bigger screen? Many, if not all, of the 4g phones have the bigger screen. But they do make it nice to do so much on. Is battery life important to you? Some phones have better battery life and some phones have the ability to have an extended battery. If you prefer a physical keyboard then the Droid 4 has a slide out keyboard. Myself, I originally thought I needed to have the physical keyboard but when I discovered swype (a method where you just slide your fingers across the letters on the on-screen keyboard and it pretty much knows what you want to type), I never touched the physical keyboard again.
Go into a verizon store that has working phones on display. Play with the phones for as long as you like. If any of the sales reps want to steer you in a certain direction to a certain phone, then let them know you want to have a chance to play with them to narrow it down and that you may have questions along the way but you just want to take your time. That is exactly what I did before I made my final decision on my last phone. I think I spent at least an hour or more in there.
Some of the phones you may want to play with are the Rezound, the 4g incredible, the Samsung Galaxy SIII (SG3), the Nexus, Droid 4, the Razr or Razr Maxx (same exact phones but the Maxx has amazing battery life), and the Bionic if they still have them on display.
My son wanted an iPhone, tested my android first before he made his decision and decided on going Android. He ended up with the rezound. He loves it, the phone reception and 4g/3g work great and it was a very easy phone for him to learn to use (and all his friends at college wanted to get rid of their iPhones to get a Rezound). The Rezound should be getting a new operating system soon called Ice Cream Sandwich (currently has Gingerbread OS) so there could be a little bit of a learning curve when it switches over to the new ICS operating system.
The 4g Incredible is very similar to the Rezound but I am not very familiar with it although I think it should have the same ease of use as the Rezound.
The Razr/Razr Maxx is a solid phone, with great reception and the Maxx has exceptional battery life. They already have the new ICS operating system so that could be an advantage to start with the new OS right off the bat rather than having to learn a new OS in the near future.
The SG3 is the latest and greatest phone with Verizon. It currently has the ICS operating system soon to get Jellybean but Jellybean is similar to ICS so I don't think there will be much of a learning curve to the new OS. It is so new that if it has any flaws, it may be too soon to know right now. So far it seems like a pretty solid phone. I think the Nexus is similar to the SG3 in user interface but I do not know much about either phone.
Hope this doesn't overwhelm you. There are a lot of choices. I think the one thing I can say, is that whatever phone you feel most comfortable to start with, you will end up being very happy with.
And if you have any questions at all on how to do anything, no matter how simple it may seem it should be, just ask and there is a whole community here that is happy to help!