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Books/suplements? None. Team rules are available in the free KT app and in a printable version on Warhammer Community.

You don't even need the Core book. Quite a few of the printed rules are already outdated. The official app -annoyingly- only has a summary of most basic rules. You're much better off using online resources like https://kt3.albecortes.com/ or https://wahapedia.ru/kill-team3/the-rules/core-rules/ as they are up to date and even provide information on which parts have been changed and link to relevant erratas and FAQs.

What you will need, though, are generic tokens, as I believe the ones in team boxes are only the ones to mark the abilities of the team in question. In particular Engage/Conceal tokens as they are key to gameplay. Once you know the game better you will see what other markers you may need - for example certain equipment options. But you just can't play without Engage/Conceal tokens (you may make your own, though, or buy them in many varieties from online sellers).

A couple of D8's and D12's to mark how many wounds wounded operatives have left wouldn't hurt either (D10's aren't that stable, that's why I recommend 8/12's)

Oh, yes, a laser pointer is very useful in KT.