Of course in the meantime, I've bought a pair of Character Class decks. My impression is that I can add them to my base game that I'm playing with my family. I would do this by just sorting everything into its space with the base game. However, if I want to bring a character to play at my FLGS, I need to keep that character and gear separate. Or could I bring one of the base set characters with me to my FLGS campaign. Or can my base set with family become it's own campaign.
Lastly, who or what should I be bringing to Gen-Con in a couple weeks. I've signed up for a couple basic sessions, plus one tournament.
Pathfinder Adventure Card Game has two "modes" of play, the home game and Organized Play. How you make use of a class deck depends on which you are doing.
For a home game, you mix in the class deck cards with all of the other cards in the box (of the appropriate number; so at first you would only mix in B cards. When you start Adventure 1, you mix in the 1 cards, then the 2 cards when you start Adventure 2, and so on). Your characters use any cards they come across, whether that card is from the base set or the class deck.
For organized play, you keep your class deck separate, and your character is built using only cards from that class deck. The Guide To Organized Play (free download from this site) explains in more detail how characters are built and how rewards and deck upgrades at the end of scenarios are handled.
I would not recommend using the same class deck for both a home game and organized play. Organized play is required to use a class deck and a character that shares a class with that class deck (which can be from a base set -- so you can use your Rise of the Runelords Valeros along with the Fighter class deck). There are also "boons" you can obtain which allow you to play specific characters from base sets alongside specific class decks, which apply to characters that don't otherwise have an associated class deck. You can earn these boons by completing organized play adventures or at conventions.
I am assuming that your FLGS is running organized play, but I would check with them about that first. Gen Con is certainly going to be organized play. For organized play, you need only bring along your class deck as well as any chronicle sheets you may have for that character. You will need to register that character on this site in order to get a Pathfinder Society number. Also, download the Guide to Organized Play and read through it, and ask any questions you may have about it in the Card Guild forum. If your FLGS is running organized play, you can use the same character for your FLGS organized play as you do for Gen Con.
You can bring along the base set if you want just in case it's needed (since each base set can only play up to 4-6 players, a large event may require multiple base sets), but it is not required. If you are running a home game out of your base set, bringing it along will likely be more trouble than it's worth because you will need to record everyone's deck and what cards were removed from the game, and then reset the base set into a state where it can be used for organized play (you can't have prebuilt home game character decks squirreling away boons if you're running an organized play scenario out of that set, so all of your character decks need to be mixed back in, and all class deck cards need to be removed from the box).
Hope that helps!
1. Home games are neither registered nor reported, you can do whatever you want with them. They are designed to be played in order, so I recommend sticking to that. If you want to add a character in halfway through the game, you are free to do so. My personal recommendation is to just give them all the same amount of feats everyone else has (the official rule is they start with nothing until they replay all the old scenarios, but that's a waste of time and not a whole lot of fun imo). Build their deck using only Basic cards if you're playing Adventure B or 1, or any card with an adventure deck number of 2 less than the current adventure if playing Adventure 2 or above (B and C cards count as 0). You can also just keep your son's character built so he can just keep the deck he previously had and jump in whenever he wants.
2. Yes, this is all detailed in the Guide to Organized Play. Unlike the home game, organized play scenarios can be run out of order, to account for the fact that not everyone makes it every time. The story is still linear, but the option to skip around exists. Pay particular attention to how the tier system works, and what scenarios you can play in a given tier. You may need to play a pregenerated character if the scenario on the table is out of your character's tier range.
3. You can run organized play at home, but if you register and report the characters you must play using all organized play rules found in the Guide. This includes purchasing and playing the organized play scenarios as well -- you cannot use the scenarios included in the box for organized play. Similarly, each character would need their own class deck, and the class decks cannot be mixed into the box.
You can also just play the organized play scenarios without following all organized play rules, but in that case you're just doing a home game with a different set of scenarios. Those characters cannot be registered or reported, and are not valid to take to other organized play events.