I mainly play as a bowman (yes - usually male characters) and back this up with dual wielding for when it gets up close so to say. The best way to take down a bowman (or almost any ranged character) is to 'shut down' that character by moving in close - and the AI in Skyrim seems to take this into account very well.
For dual wielding, my usual setup is an axe with a fire enchant (targets on fire receive harder hits) as primary and a mace with a 'soul trap' enchant as secondary - maces are somewhat slow but they do tend to hit hard. The enchants are used as soon as available to character.
I also usually carry the best dagger available to my character with a suitable enchant as this can have its uses when sneaking! My armour is always the best light armour available to my character.
As a bowman (character), I find archery, light armour and sneak perks get a lot of attention and back them up with one handed perk and then go to supplementary perks such as the very useful smithing and enchanting.
As for 'What's the best set ...', this really is a personal choice thing. You could try playing a test character and try the different setups to see which you are most comfortable with. Which ever way you go, I hope you have fun.
Edited for some spelling errors and one hilariously badly spelled word!