equipment, general appearance, fighting style, all that.

What do you mean by freelancer? Do you mean a mercenary?

The Mercenaries you occasionally run into on the roads might be a good bet; go to an inn, find a bounty, and go out and kill whatever needs killing.

I think I'd go assassin style, twin daggers and a crossbow if you don't want to join the Dawnguard at all then use a bow.

Archery, stealth, light armor, 1h (dual wield), alchemy.

When I think 'freelancer', I tend to think - "the most generic/common character build possible" (sorry, I'm only joking )

But seriously, I find it semi-difficult to suggest build specifics in this case.

It's like asking for help in creating an 'adventurer' build. (ie, uses armor and weapons, maybe magic... drinks potions...... likes earning gold...)

Anyways, maybe if you can give us some more specifics of what you had in mind, I'd gladly throw out some suggestions.