It's been a while, but I believe that I got archery up to a acceptable damage level, while also focusing on stealth equally.
The unfortunate part of this build is you also need smithing (what build don't you I guess, maybe a caster) to make better daggers and bows/arrows.
Join the dark brotherhood and get their gear ASAP. For the back stab gloves and other shit that helps(vague, but like I said, it's been awhile)
Don't forget to find jewelry that increases archery damage/sneak.
You can use poison to coat the arrows, but don't start building up alchemy right away, get sneak and archery high first.
Don't worry much about armor, if you sneak good you'll hardly ever get hit.
That's all I remember off the top of my head. Hope that helps.