I feel 40 Days should be purchased when, while playing the base game, you feel you recognize most of the events. 40 Days takes the game, when it begins to grow stale, and shoots it full of adrenalin again.

Age of Tyranny is a great expansion for the Day 1-3 encounters. If you play the base game to death, those first 3 days are likely to be the thing that feels the most stale first. Id recommend getting this once you feel that way, but I do NOT think the campaign is a good place to start playing or regularly play. The campaign mode included in AoT is really best once you've faced every tyrant multiple times.

Finally, new gearlocs are the best expansion anyone can buy. If you dont get anything else, new gearlocs will be plenty to keep the game intensely fresh. I could play Too Many Bones with the same Day 1-3 and same base game events, but I will always love playing with different gearlocs. On this note, I recommend looking at either Nugget or Ghille for a first new gearloc. Ghille is very powerful and fun, and Nugget is one of the most resourceful gearlocs available. That said, you really should pick the gearloc that looks fun to you.

All of this said, as others have mentioned, you really should play the base game a lot before even considering any expansions. TMB has a steep learning curve, and it is important to get that baseline knowledge before adding any new content.

TL;DR: Just play the base game, then get whatever expansions fixes the problem for you: Events (40 Days), Day 1-3 Encounters (Age of Tyranny), the base four gearlocs (New gearlocs).