Mount and blade series is great.
Though Mount and Blade warband (basically an upgraded version of the original) is the best and still has an active multiplier community if you want that as something else you can do, also has quite a cool official Napoleonic expansion. Most people would suggest give fire and sword a miss, so would I for that matter, only bother with it if you find the era interesting. Mods for the game is great for multiplayer, but this game is great at singleplayer, though it explains itself even less than POTC build mod
It is possibly the closest your going to get seeing it has all the features your stated and you can eve hire troops to follow you.
I have to admit mount and blade 2 bannerlord looks like it's going to amazing!
Chivalry: Medieval Warfare is 'okay' just it's multiplayer only and the combat does not seems as intuitive or as realistic as M&B.
Give it a go if you have cash to splash... but it has no singleplayer.
As someone said, kingdom come....
Skyrim actually if you don't mind fantasy, I do remember a historical mod some time ago but unsure if it ever got finished.
There's not actually many medieval games of the kind of style your looking for, most are fantasy. While M&B is technically fantasy (apart from fire and sword) it's just a made up continent with factions closely based on real life equivalents (aka norse, english, french, italian, slavs, arabs & mongolians) and does not use magic etc.
However if you like intrigue Game of thrones style look up crusader kings 2. Or Medieval 2:total war, if you want it on a much lesser scale but with realistic battles with thousands of people.... both games are great to role play being the faction leader... in fact Crusader kings 2 actually requires you to have a Role Playing mindset. However both are strategy games
The total war series is kinda my specialty though
hell Empire & Napoleon Total war even have gunpowder era naval combat
Actually thinking about it shogun 2 has an standalone expansion that has 1860 naval combat with american and European Ironclads.... but i digress