^ yep, buy what you need as you need them. I find the tool kits contain a lot of things you won't ever use and a few essentials, and then there's a tonne of stuff you can do with standard household tools. Specialist stuff depends on the components you use. I find it helps to pick a standard and stick with it.
Key things though I'd say are getting *good* quality cable cutters if you're going to do brake cables & good quality allen keys as cheap ones round things off easily (and a torx if anything has torx bolts, probably just a T25 is needed). BB tool appropriate to your BB if you're likely to do the BB. Likewise whatever for the cranks or if you're lucky it's all allen key stuff (like GXP).
Chain whip and cassette tool.
A good ratchet wrench and worth considering investing in torque wrenches (you may need two for high and low torque), or otherwise learn to judge the torque needed. A lot of issues people have are due to incorrectly torqued components, too weak or gorilla handed.
Grease (not lithium based) for bearings and stuff that need to move, thread lock for small bolts that need to stay in place. Carbon paste is handy too even if you don't use carbon components. Recommended with stuff on the bars and the seatpost just to reduce the clamping forces required and stop slippage, and essential for carbon.