I prefer boots for jumping and polos for flatwork. Only use polos if you have been taught and are confident using them, as they can easily damage your horses legs. I used open fronts($20) for the front, and woof for the back, plus bell boots when jumping in the ring(my horse has a BIG and clumsy stride). Bell boots were $10, woof boots were $30. When going cross country or on trail(and we are jumping) I like my dalmar eventing boots so far. They were a bit pricey($80) but I really like them the few times I have used them.
SO I guess I think you should boot up.
On a side note, I don't reccomend jumping your 7 year old horse up to 3ft 6 times a week, no amount of boots and wraps are going to protect his legs from that much constant concussion.(no offense intended, take this with a grain of salt please)