In order to get the most out of your kicks, you'll need a heavy bag or some other kind of kicking target. The idea is to not aim for the target but aim several inches into the target... you want to kick through the target each kick. There is also the idea of kicking from the proper distance to generate the most power as well... practice makes perfect here.
Practice each kick with about 10 to 20 kicks each leg (kick as hard as you possibly can each kick) each workout then as your shins and feet get better conditioned, start doing 30 or more kicks per session.
If you use a heavy bag like I do, you can tell right away if a certain kick (roundhouse compared to front snap etc, etc)has power or not and you can concentrate on the weaker kicks in order to get them as strong as possible.
As far as weight training goes, you may end up disappointed with your kicking power compared to kick training.
Practice your kicks 3 to 4 times a week and you should start seeing positive results in about 4 to 6 weeks.
As far as kicking height, you need to stretch for this or you'll end up getting your foot up there but with little or no power behind the kick... not good
Practice for height the same way you practice for power and kick only as high as you can and still be able to deliver power... you'll notice over time that your kicks will go higher and still have power, this doesn't happen over night either, but you should see progress in a few months or so.