I used to own a JP7 with no options and a UV777BK. I have never owned a UV7BK but I did rescue a UV7PWH from Guitar Center which is from the same era. (Just to be clear, by rescue, I mean I paid for it and got it out of the store.)
The UV777BK was my dream guitar! There is something to be said for owning your dream guitar when it is still your dream guitar. The mirror pickguard can crack, particularly from guitar techs tightening volume pots too tightly, and they are really expensive pickguards to replace. This is not really a problem, just an unfortunate event. I feel like the Pyramid Inlays were not inlaid as well as they could have been. There seemed to be black glue around most of them indicating the pyramids were too small for shape cut into the fretboard. I have seen better inlays on other Universes, including other UV777BK's. With that said, I played that guitar the most of the three and I am glad I owned it when I did.
The Music Man JP7 was a great guitar! In terms of build quality, I would say it was the best of the three. I learned I prefer a H-H pickup configuration versus a H-S-H configuration. The JP7 was not a particularly exciting guitar. It was built extremely well, reliable, easy to play, sounded great, but I almost never reached for it first.
In hindsight, the UV7PWH was a better guitar than my UV777BK for three reasons. First, it was in Mint condition. Second, the neck was incredibly thin. Third, it sounded better. However, the fact it was in Mint condition meant I wanted to keep it in Mint condition so it lived in its case in my closet the majority of the time. I rarely played it because I was afraid I would put the first nick or scratch on it. I eventually traded it for a guitar that I played a lot more and was probably of equal value at the time. When I owned these three guitars, the UV777BK was still in production and UV's were not collectible like they are today.
If I were in your shoes, based off the information provided, I would go with the UV777BK. It has a Lo Pro Edge 7 and you probably will not be buying it off a smoker on old-school eBay. I would go with the JP7 second because it is probably a solid and safe choice. The bridge is really good but has a much different character than the Lo Pro Edge 7. It is more subtle and does not dive down or pull up in an overly dramatic fashion. Third, I would choose the UV7BK because you could be getting a great guitar in good condition, a flawless guitar in perfect condition, or a beater that has been abused. (I've seen one in such shape before.) Ultimately, you are choosing between three guitars of equal quality, more or less. If all else fails, base your decision off looks.
I will say you are buying your first 7 string the right way!