Cheapest = rogue
But I think that the best starter character is a fighter.
For gear to use, you always want EE on your weapon, EE or stats (str/dex) on your armour, and stats on your main charm (str/dex)
At level 1 try to get tier III items with 40+ ee and 10+ of either stat then work up incrementally from there.
Something like this would be a good starter set:
Weapons:
Level 0: 40 ee
Level 5: 50 ee
Level 10: 60 ee
Level 15: 70 ee
Level 20: 75 ee
Level 25: 80 ee
Level 30: 85 ee
Level 35: 90 ee
Level 45: 95 ee
Level 50: 100 ee
Level 55+: 100+ee
Charm:
Level 0: 10 str/dex
Level 10: 15 str/dex
Level 20: 20 str/dex
and so on
Armour:
if using ee armour then follow the same as weapons
if using stat armour, follow the same as charms
Those numbers are by no means set in stone or anything, but should be though of more as a rough guideline. You could easily get by with significantly lower gear, and you would be able to kill better with higher statted gear.
Nothing is reset when you attempt the MQ except for your character level. You keep all items, objects, proficiencies, kills, deaths, etc.
The easiest way to stat a melee character is to just put every point into strength when you get it. Another viable way is to balance your points between strength and dexterity keeping your strength ~20 points higher, but I think that all strength is not only easier but also more effective.
Hope that helps a bit