I think there is plenty of good advice above.
I recommend augmenting your bow with either blade or magic (both if you want). It sounds like you want marksman as your primary killing skill and to back it up with a blade. Here are some things such a character might consider:
- Take marksman as a major skill and try to bump it up at least 3 skillups for every time you level. When you level up, try to improve your agility attribute. Those things will help keep your lethality going up as quickly as enemies gain hitpoints as you and your foes level up together.
- As SubRosa wisely said, get good with sneak and poison - learn 'em and use 'em.
- A bow? Use the best available regular bow available for your level. Once you can repair magic items and capture souls (Azura's Star is very handy here), then enchant your bow. You did use the time learning to repair magic weapons to get into the Arcane University so you could enchant your own stuff, right? Since you are using a blade as your back up, you don't really need to immobilize your foes (like a no-melee mystic archer loves to do). Therefore, I would enchant your bow with a 1 second soul trap and plenty of elemental damage.
- An archer who uses a bow as their primary weapon does best with a slow, methodical playstyle. Plenty of detect life and snooping around and selecting firing positions.
- As far as build stuff, gee it just depends on so many variables and things like how you want to play, how fast and high you want to level, how 'uber' you want to be, what kind of image you want your char to have, what you want them to wear, how much you like to use certain skills and so on. Therefore, I generally stay away from specific 'how to build a good xxx' questions.