Read my post at the top of page 14 for a description of Soul Gems and how you use them
Just use the bow a lot. It's easier when you're sneaking around as you can get a bit closer to you enemy to shoot him. Fire one arrow off for extra damage, he'll get hit and run for you, then put at least one more in him while he closes the distance. Switch to your melee weapon for when he's right on top of you. My marksmenship is over 50 now without having it trained once.
You really can play it your way. Follow the main quest line, or just wander from town to town talking to people and doing random quests. I'm about 40 hours in and I've only done 2 extra parts of the main quest to you.