[RPG] Player character wants a gun in a prehistoric campaign. What to do

Oracle is a spontaneous, divine spellcasting class. She has a greater number of spells per day than a Cleric, and can cast without preparing in advance; but, she has a narrower list of spells that she can choose from. She is the divine equivalent of a Sorcerer (whereas a Cleric is comparable to a divine Wizard).

Be mindful that Oracle isn't especially tuned for making ranged attacks (though she isn't terrible); as you level up, if you find that ranged attacks are your focus more than spells, you may want to consider multi-classing into a prestige class that gives you a higher Base Attack Bonus while continuing your spell progression (Eldritch Knight is a good example). On the other hand, you may decide that you want the Oracle's neat higher-level class abilities (Revelations, etc) more than you want a couple points of extra attack bonus.

Abilities:

Key ability: Cha.

Your key Ability score is Charisma, since Cha gives your spells a higher save DC, limits the highest level of spells you can cast, and grants you bonus spells per day.

For ranged combat, you also need a high Dex. Dex also improves your ability to dodge attacks, and increases your Reflex save (resist fireballs, traps, etc).

Con gets you more hit points, and a higher Fortitude save (resist poison, being turned to stone, etc).

Str won't be very important to your character, except to carry gear.

Int grants you more skill points.

Wis gives you a higher Will save (resist mind-affecting spells, etc).

Skills:

Look through the class skills to figure out what interests you. You should have max ranks in the Spellcraft skill. You can also choose cross-class skills without a big penalty in Pathfinder, so you should skim through the entire skill list to see what's available.

As a rule of thumb, I usually pick a number of skills equal to the number of skill ranks I get per level. For example, if you get 8 skill points per level, you could put max ranks in 8 different skills. If you decide you want more skills than that, you can split up one "ranked skill" into two "half-ranked" skills, and put a half-point in each every level. This isn't a hard-and-fast rule, just a way that I've found of making the decisions and the math much easier.

Feats:

The Extra Revelation feat is an Oracle-specific feat lets you choose an additional optional ability from the list for your chosen Mystery.

Since your character is heavily involved with ghosts, I think the Ectoplasmic Spell metamagic feat from Advanced Players' Guide would be appropriate.

Beyond that, feats which enhance your spellcasting will be the most effective for your character; since you are doing ranged combat, you will have to split your feats between ranged and spellcasting. I would recommend reading through the table at the beginning of the Feats chapter (both in the core rulebook and the Advanced Players' Guide) to get a brief description of what each feat does; there are a lot to choose from.

If your group is more familiar with 3.5 than with Pathfinder, remind them that you get a feat every 2 levels, not every 3 (so you should have 3 character-level feats at level 5).

By RAW, your second option is the correct one: a musketeer who wants to use a firearm other than the musket/pistol given by his order can only do so by ignoring his ability to focus with his gifted weapon. There's nothing that I can find that replaces a cavalier's gifted weapon with an advanced firearm.

However, you should probably talk to your DM about this. Assuming advanced firearms are allowed in your game, I would suggest asking your DM if you can simply pay full price for the advanced firearm out of starting wealth, and have that gun be your gifted weapon.

It makes some sense to me that a cavalier order may give less powerful guns to newer recruits, and allow more experienced members the ability to donate a fee to the order to gain the right to wield a more powerful weapon in their name.