I'm worried about the boots, too. The heel is OK. But I think that the zipper on the inside of the calf is going to scratch the tack - and the stirrup leathers are going to scratch the boots. I also suspect that you'll find it very uncomfortable. Boots with that kind of sole - not with the chunky lug sole that your winter boots have - and that height of heel, without a zipper on the inside, would be the best.
Even before the breeches, you might want to invest in a pair of paddock boots and half-chaps. This will definitely not mess up the tack (or your boots) and be a lot more comfortable. Paddock boots are short boots with the right kind of sole and heel - they are designed for riding. They're usually a little above the ankle, and they either lace up, or zip up.
Like this: http://www.doversaddlery.com/images/300/38508.jpg
You wear them with a pair of half-chaps. These are like sleeves that fit over your leg from the knee down. They usually have a strap that goes on over your boot, right in front of the heel, and they go up to your knee, and most of them zip - on the *outside* of the leg. Most of them also have a reinforced spot on the inside of the leg where the stirrup leathers are going to hit your leg. They go on over your pants.
This is a picture of someone wearing paddock boots and half-chaps. It looks like she's just wearing tall riding boots, but if you look closely at the picture you can see the strap that goes under her boot. http://www.doversaddlery.com/images/300/35317.jpg
Paddock boots + half-chaps gives you everything you need to ride English until you want to start showing or decide it's time to invest in a pair of high boots. Your folks will be happy because this is much cheaper than the tall boots, and when your foot grows, you can replace the boots and keep the chaps (and if your leg grows, you can replace the chaps and keep the boots). If I had a kid who was taking riding lessons this is what I would want them to wear. It's also what I wear myself. :) I've also found this arrangement to be easier for me to find a set that fits properly than it would be to find that in tall boots, and I find them a LOT more comfortable than the tall boots I have for riding in the winter.
Breeches are sized by your waist - you would measure that, and then look for a pair of breeches that has that same size. They all fit kind of differently, though, so if there is a tack shop near you, you should think about going over there and trying on a few pairs so that you will know what style/brand/size fits you properly. For me, I've tried maybe 6 different kind of breeches, but the only ones that fit me right are Tuffrider low-rise breeches, even though I am trying on the same size in all the different brands. And even then, Tuffrider non-low-rise breeches don't fit me as well even though it is the same size and the same manufacturer. So it is definitely worth spending a little time trying stuff on.