I hunt public close to my home sometimes. It's archery only and there are a few people who hunt it. Public land is one reason I have a few of those $50 Tasco camera's from Wal-Mart. Since I tend to hunt the nastiest, thickiest recesses of public land, I don't have a lot of problems with thieves, although I've had a few stands stolen in the past.
These cheapo trail cameras are not the greatest camera's on the market, but it beats nothing at all IMHO. I simply use them to confirm what I already suspect about an area or to help me tweak a stand location.
Sure, you'll get the blackouts for no reason or pictures like this one...
But then again, you'll also get pics like this
Not bad for a $50 camera. And if it get's stolen, I at least know other people are in the same specific area. Who knows, maybe you'll find out a few of these live in the deep darkest corners of your local Public hunting spot...
Of course, if you want to put out your $200 Trail Camera on Public land, go ahead. I save those for the Private property I hunt

Now therefore take, I pray thee, thy weapons, thy quiver and thy bow, and go out to the field, and take me some venison; And make me savoury meat, such as I love, and bring it to me, that I may eat; that my soul may bless thee before I die. Gen 27:3-4