The new game played solo and played with both sides are pretty much the same experience - the solo rules offer very little in the way of lessening the burden of operating the
NPCs, as most of them need to perform exactly the same actions in exactly the same way
PCs do. Only their stats are simplified in comparison. So you really just spend as much time performing automa moves as your own. Not the best design
tbh.
Check either the Kill Team App or these documents :
https://www.warhammer-community.com/en-gb/articles/xfV8vUOg/download-the-kill-team-app-and-faction-rules-today/ for team rules. Out of your armies the one that will most likely have all the models for a player-run Kill Team are Imperial Fists (Angels of Death kill team). Use other armies as
NPCs for solo/co-
op. Once you get some experience with how the game plays, it will be easier for you to see if you can construct other Kill Teams from the rest of your collection.
Core Rules rulebook should be enough to get you going, although some tokens (at least order, ie Engage/Conceal activation tokens) would be really useful. You can replace them with some markers for your first games, but the game will probably run smoother and the board state will be easier to read with dedicated order tokens. Oh, the board itself could also come in handy, so that you can easily set it up without taking measurements to limit the playing area on a bigger board every time.