There are a lot of questions here. I'll try to answer the overarching one(?), "How best to make a bow/unarmed character?".
Firstly, lets get some misconceptions out of the way.
I read that doing the vampire quests from Dawnguard gives you access to a perk that adds 20 poison damage when striking with your fists
This only works when in the melee mode of the Vampire Lord form. In Vampire Lord form, you lose equipment and racial bonuses.
... I don't want to use heavy armor. So I will not use the "Fists of Steel" perk.
Fists of Steel doesn't only work on Heavy Armor. You can simply train Heavy Armor at a skill trainer just high enough to get Fists of Steel and wear Light Armor and get the +glove-armor-to-unarmed-damage benefits anyway.
Gloves of the Pugilist
Disenchant if you want multiple sources of this bonus damage. It can be applied to rings, gloves, and gauntlets. If you want unarmed to be anywhere near meaningful at around level 50-90, you probably want this enchant as much as possible, especially since you won't be going Heavy Armor.
One of my favorite specialties. It sounds like you're not really concerned about this aspect of your build, but I would like to put in a good word for using poisons with Archery. You can paralyze enemies and eliminate mana pools from afar in addition to doing massive amounts of extra damage.
If you take my advice and pick up Fists of Steel, Smithing is a critical skill. Make yourself some Dragon Scale armor and use potion/enchant stacking to refine it as high as it will go. Without Fists of Steel and this armor stacking strategy, your unarmed ability will be next to useless at around level 30-40.
Don't be afraid to dip into skills that you don't necessarily want to specialize in. Some low-level perks make a world of difference for a nominal training investment.