Kill team doesn't use the base game codexes. The datasheets for individual units are in the 3 books. Datasheets often differ significantly from their base game counterparts due to the rules changes, and points can vary wildly from their 40k counterparts. Things are generally cheaper, but there are some exceptions out there.
List building is one thing I didn't mention. For tournaments and leagues, you build a roster of 20(? I think? This is what my local leagues use) models. The only restrictions in Roster building are;
A) You need to be able to build a legal list from said roster, so you need at least 1 Leader specialist
B) No more than 1 of each commander datasheet
Once you and your opponent set up to play a game, you choose models from your roster to assemble your kill team (100 points for core games, 200 points for Commander games, 100-125-200 for elites), based on knowing each others' factions.
Vehicles are just terrain, yes. As for first purchases, the core rulebook will get you all the basic rules you need. Battlescribe can largely sub in for elites and commanders, although you won't have the tactics. If you do buy commanders, get the e-book. The physical bundle is comically overpriced ($25 for the base e-book vs. $60 for the physical book, a tiny sheet of tokens, and some reference cards).
The starter sets (The big 2 faction box as well as the smaller 1 faction boxes) aren't necessary, although they're not bad deals if you want all the models in them. The kits (as well as the little commander boxes) do contain a few "exclusive" tactics, but outside of a GW store, I highly doubt anyone will object to you going on 1d4chan and copying the exclusive tactics onto flash cards. Plus, a lot of the exclusive tactics from the starter boxes got printed in Elites anyway.