As usual, my step-brother in arms has shown his prejudice against the single shot rifle that was acknowledged by the market as the most popular of all times (from a commercial point of view) the Winchester Single Shot in high- and low-wall configuration. With over 130,000 of them sold, they are the undeniable champs in popularity. Only the military rolling blocks and trapdoors are more numerous. That said, the well equipped single shot enthusiast has an easily identifiable number of rifles that he needs at any given time, "just one more!"
I personally find it absolutely necessary to have a good offhand rifle, a good bench gun, of course an over-40 cal rifle or two for schuetzen which may or may not also be used for BPCS and or Creedmoor, then of course a quarter bore or two, several rimfires for all of the various events in which they are used, and hunting rifles for small game, varmints, medium to large thin skinned game and then something really big for that dangerous game I may one day get to hunt. I'm sure I left out something, so of course I will always need "JUST ONE MORE!"
All kidding aside, Mr. Sharps 1874, the rifle you have coming is one of the best and most versatile single shots known to shoot a variety of targets, some better than others. You might want to look into a .22 adapter so that you can shoot it A LOT without spending time casting and loading. Then if you get interested in schuetzen, or one of the other specific games we play, you will have the experience and will have developed the discernment to pick out what will work for you. (But don't forget to look hard at the 'walls!) The Winchesters (original and copies,) the Ballards (ditto,) and the Stevens, especially the 44 1/2 originals and copies join your Sharps and its successor the Borchardt as the most popular. The aforementioned rollers and 'doors also have their supporters and niches as do the modern single shots and some of the less known early ones like Maynards, Wessons, etc. Don't forget the various European models, such as the Martini and the various German models like the Aydt and Beuchel. There are so many different rifles you can eventually find the ones that do just what you want them to (unless like me, you find another one that also piques your interest!) HTH, and as always, YMMV!
the Green Frog