I hope you have the best first con ever! I've been going a few years now, and this is what I passed on to some friends that are going this year for the first time as well!
Vender Hall: I definitely recommend taking at least a day in order to check out the dealer hall. Thursday is the least crowded, and you have the best chance at getting that must-have game from the con :) The hall is simply enormous, and as you are wandering there is a fair chance that something will catch your eye; a demo, some amazing art, a celebrity. Just be prepared to be on your feet for a solid afternoon at least if you want to see everything, and prepare your back (and your wallet!) for all the games that you'll have to haul back to your room or your car if you plan on doing any shopping. If you want to save your wallet some grief, you can occasionally get some great deals from the vendors on Sunday, but its a gamble as to what’s going to be left over.
Food and Water: I generally just pack a small (small! really!) bag with enough to last through the day and try to find a restaurant for a larger meal either around 3:30-4:00 or from 9:00-midnight. I find that 3:00-4:00 generally works out the best. Remember that anything you pack you have to haul around all day long and you need to remember to keep an eye on things. For water, I would bring a small water bottle along and refill as needed. There are many, many fountains about and water this way is free. If you buy a bottle of water (GenCon rates may make you cringe!) hang onto it for refills :)
Speaking of a small pack to bring: aside from some light snacks and water it can also be useful to pack a mild painkiller for anyone that gets a head or back ache (Aspirin, Tylenol and the like) as well as HAND SANITIZER. There are going to be just a ton of people everywhere in various states of health and it helps tremendously to have some hand sanitizer to use before you sit down and after you get up. After my wife made this suggestion I've been con-plague free. Others will be grateful to see that you’re using it as well. I would also recommend a little bar of deodorant, breath freshener, and a fresh t-shirt and socks in your pack to round things out. Something I don't recommend bringing is a cell phone charger that needs to plug into the wall. Instead one of those battery-pack refill things are great for the con. Plugs are hard to come by and root you to a single spot for an hour. The refill packs hopefully will keep you topped off enough that you can keep on con'ing and will free up outlets for others.
Must do's: So, there are two different schools of thought on GenCon must do's. For the ‘completionist', I would recommend you visit any panels put on by any names you recognize (this can change from person to person, for me its Shut Up and Sit Down). If you see a name you like having a panel, jump on in! The other 'big' events that stand out to me are the True Dungeon, AEG Big Board Game Night (you get to go home with a free box of games that more than make up for the cost of the event), The Killer Breakfast (Not sure if they'll be doing this in 2017), Drunk gaming at the RAM (best part about this is getting food and a table at the RAM, which is nearly impossible to do at GenCon otherwise), and NASCRAG. Others I'm sure will fill out the blanks.
But here's the thing...
In my personal experience, the best thing to do at Gencon is to book one, maybe two things that you want to do a day and then to make new friends and find new events to go into. To get into most of the 'big' stuff you'll need to be at home on event registration weekend (and this year that’s Memorial Day, May 28th) and mashing the 'refresh' button on your browser and hoping that you get low enough in the que that you'll be able to successfully get into these events. It can be stressful and there are no guarantees that you'll come in fast enough to get registered for everything. So I usually just say go with the flow.
I hope you have the best Con ever and remember it for years. The only other thing I'd like to add is that GenCon tends to attract a hugely positive, welcoming group of people compared to other Cons. If you ever want advice on the next thing to do, ask an excited looking stranger and see where they're going! I've found so many amazing events I'd have never known about using this method, and I have been repeatedly grabbed by the arm and told "You've gotta see this!" and whisked away. Welcome to the community!