There have been some great suggestions so far, I just want to add that if golem is also on the board, I like to grab as many golems as I can, a couple possessions, and minimize other action cards.
The player possessing you will not be able to resist the temptation of playing your golem which will draw one or two possessions!
I once played a game where my opponent grabbed 4 possessions and 6 alchemists.
I countered this by buying two possessions, after which I immediately started greening my deck. My opponent was completely frustrated when she was possessing hands full of green while I was possessing her more powerful deck.
I had luck on my side that game, but I ended up getting 7 out of the 8 provinces, 6 of which were obtained by possessing her.
Thus, even though she had more possessions than me, my possessions were far stronger..
It's common for possession happy players to think they can use possession to make their engine stronger.. but if you green early like other players suggest, you will leech of them and contribute little if anything to their precious engine.