I usually take in this order of priority, though of course I'll deviate if there's a perfect spot.
Militaristic (You usually get the most "free troops" with this purchase, valuable early on, and late game if there are any left, I'm usually disbanding/selling their gifts)
Religious (I'm usually not going for religious enabled/enhanced victory and would rather deny AI +faith)
Mercantile (Happyness is important, but I'm usually small/tall and happyness isnt an issue)
Maritime (I try to save Maritime CS's to ally with, love that 50 pop Venice! I usually only have Venice + 3 Puppets, who send back food trade routes to Venice, and keeping Maritimes around as allies mean I get really tall in all cities, but Venice gets BANANAS tall, great for all that GPP)
Cultured (I almost never buy these with the MoV, I feel like they are the most valuable to keep allied, since culture is harder to come by now, and getting these allied ASAP denies culture to the AI, which is usually necessary if you have another AI on the map going for culture or diplo victories) but I also love having a lot of Social Policies so mileage may vary.