Pathfinder-1e – Exceeding 18 in Core Stats at Level 1

Sure you can, as long as you meet the prestige class’s prerequisites. The Commoner class does not have any special rules about its advancement, it’s just a particularly weak base class.

It’s actually the easiest way to enter the Survivor prestige class (Savage Species), which requires that one’s highest base save bonus be lower than one’s character level. In a similar case, the Adept is the easiest way to enter the Hexer prestige class (Masters of the Wild), since it requires lightning bolt as a divine spell, and neither clerics nor druids get it, nor is it found on any Domain (amazingly).

I would comment that a common way to handle games where you start as Commoners is to have you “trade in” Commoner levels for PC-class levels, to avoid you taking pretty serious hits to your abilities relative to your nominal ECL. This is a non-issue if your DM knows how to compensate, but it might be worth mentioning as an idea to your DM.

#3 - Players typically purchase their starting gear from the gold they are given at first level. The SRD has a great article on character creation, and equipment is under section 8. The gold you have listed is, according to the SRD, actually the average for each class. As a DM, you can choose to give them the average for first level, or make them roll.

It would be good for them to look at the pre-bought sets the describe, so they can understand what's typically needed. Once they get more comfortable, they may branch out according to how they like to play their character.

Of course, as the DM you may overrule this and force them to start with a certain set of items, or give them more gold, etc. Seeing as this is your first time playing, however, I highly suggest sticking to rules as written since this sort of overruling may very well have unintended side effects.

As an aside, wizards get so little at first level because they don't need (and cannot wear) armor, nor do they need expensive weapons like swords and bows.