When we used to go to parks I would avoid off leash areas, I remember last summer me and a girl friend both experienced with dogs were walking Harley and we came across an off leash pit puppy. We have nothing against pits, but realize they take ALOT of training, and this puppy just ran up to us, jumped on my friend, licked her, then tried to jump up to me (who by now was holding Harley close in my arms) and the owner did nothing...and the puppy was HUGE
We both agreed that poor puppy would likely be branded "one of those pit bulls" when he grew up cause his owner was clearly an indiot and didn't care to train him.
So I guess I just caution you to assure that you never let your baby off leash until they have a RELIABLE emergency recall, and be cautious of the idiots with big dogs who don't care who their dogs jump on or disturb, cause you will likely meet hundreds of well trained dogs and owners, but it only takes one fool to mess everything up. I didn't really answer your question on which type of park, lol, if I had to choose it'd be a people park unless I knew every dog at the dog park (and the city I'm from that's actually possible cause it's small here and we know all the dog people).