The core book is pretty complete in its own right, although I find that BRP works better the less of it you use, and plenty of it can be ignored once you've got the basics down (very easy). Nothing else is really essential: it even has some short scenarios, although which ones depend on the edition. By the way, I don't think it matters at all which edition you get. The rules have had some minor adjustments, but nothing you couldn't house rule - and BRP is very much a house rule-friendly system. Get whatever is cheapest, preferably 2nd hand.
For a few books more, it really depends what setting you had in mind.
For Lovecraftian New England in the 1920s, the Arkham and Kingsport setting books are very good, and the Investigator's Companion has useful period details. I don't have Dunwich, but I hear that's pretty good too. But if you were thinking of setting stuff in the UK, then very little of that will be useful.
If you like the UK Victorian period, I would recommend waiting for the next edition of Gaslight, due out soon. It throws out a lot of Holmesian stuff and adds a lot more period detail, and some pretty decent scenarios. Unless you really want lots of info on how to incorporate Holmes into your CoC, which I think is mostly pretty obvious anyway.
As Viktor says, if you want modern day, than Delta Green has to be worth a look, although it's not something I've ever used.
Other good period choices also exist, but are less well supported at the moment, although 1770s should be a fun alternative when Sixtystone Press get to publishing their planned series of books.
Dreamlands is very much a Marmite thing. I enjoy it, but lots of people don't. I think it's stronger when mixed in with something else. Not recommended initially.
Regarding campaigns: Masks is a blast, so long as you like things a bit pulpy. I haven't run BTMoM, but it has amazing potential if you can get players who will commit to a game of that length and enjoy the (very) slow burn. I enjoyed running Horror on the Orient Express and Spawn of Azathoth, but there are things about them that need fixing. There's a lot of love out there for Tatters of the King, but I have yet to run it, although it looks very promising. Ditto Escape from Innsmouth, unusual for its troupe-style play (that one is more of a mini-campaign compared to the others).
You will already know from ToC that Ken Hite is an amazing source of inspiration and advice. Almost anything of his is worth a look. Dan Harms' Encyclopedia Cthulhiana is also handy for instant info on Mythos canon, if you can find an affordable copy.
Beyond that there are plenty of history books I've found useful over the years. But it does depend on the setting, obviously.