I run H2's with my 14.5" middy's but that doesn't mean that it will work for you. Start with a carbine buffer and go from there. Once you break the rifle in, then decide if it needs a heavier buffer. If you feel that it does, get an H2. If the H2 is too heavy, you can swap one of the steel weights from the carbine buffer with a tungsten weight from the H2. Essentially making a H buffer.
Carbine buffer has 3 steel weights
H buffer has 2 steel and 1 tungsten weight
H2 buffer has 1 steel and 2 tungsten weights
The BCM tubes are excellent as well as their buffers. Also use a standard mil-spec carbine action spring. The only time I have run into cycling issues was when using fancy NASCAR springs. Buy a half dozen or so and you'll be good to go for quite some time.
I'm not sure what the ST-H is but if it's like the ST-T2, it won't do anything better than a H or H2.