Are your feet done growing? If they are, then maybe go for the tall boots. If not, probably half chaps. I have never had synthetic tall boots, so I don't know how comfortable they would be. Maybe make you really sweaty, I'm not sure.
I personally really like riding inhalf chaps and paddock boots. I think it might be better to just go with that for now, and try to begin saving for nicer tall boots. Then when you have $200, you can get good tall boots which should last you several years, and wear them when you want to "dress up" but you will still have your paddock boots and half chaps for muddy days or schooling or whatever. That combination works nicely for me.
Just check with the show to see if "schooling attire is permitted" if it doesn't say that, you may have to have tall boots to be dressed appropriately.