First of all, welcome to Wizard of Vegas, Aimee, and I hope you enjoyed your 21st birthday. While all birthdays, 'Only happen once,' that is definitely the big one.
You can learn about games at Wizardofodds.com and you can learn about the different casinos with hotels in the Reviews on this site. I believe that almost all casinos with hotels have been reviewed here.
I would recommend obtaining copies of the American Casino Guide and Las Vegas Advisor before going to Vegas, they are full of all sorts of useful coupons, many of which are for Free Play or table game Match Play which will give you the opportunity to play many different games. Do not use a Match Play (or play at all) on Blackjack if the table pays 6:5 on a Natural, you want the Table to pay 3:2. If you have a Match Play and only want to bet the Table Minimum, but it is a 6:5 table, make your bet on Craps instead, either bet the Pass or the Don't Pass.
If you tell them it is your first time ever playing Craps, they may well pass the dice to you so you can shoot at earliest opportunity. The earliest opportunity would be after the current hand has finished. Many players consider a female first-time (apologies if my assumption based on your handle is incorrect) Craps player to be good luck. It's not actually mathematically true, of course, but if it were me I would skip my turn to shoot out of deference to the superstitious ones. It's polite to a first time player to give them the dice if either he or she wants them anyway, I would suggest.
Other than that, I've got no further advice for you at this time, other than to check out WoO. Video Poker is better than slots. Try to play a good bit if you are staying at a casino's hotel and they might comp off some or all of your room charges, but don't play for JUST that reason or beyond what you can afford.
Many casinos offer benefits for new players club members, but it is up to you whether or not you want to do that. In many cases, it would be better to wait for a better new player offer and not take the first one that comes around. Keep in mind that would also prohibit you from doing some of the Free Play coupons if you do not want to join the players club at that casino. I think there are also a few places that you couldn't get your match play down without a card, but not many. Cannery is one that would not let me play my match play without a PC card, of course, they didn't say that until I had already bet it and won.
If there are any specific games you may have observed that you think you might be interested in, then you would do well to say so, and some of us could more specifically direct you to the pertinent information.
Also, people with no players club cards are often a hot commodity. You might receive a few PM's when you post a more specific date that you are heading out there, and perhaps even before that. Most people here can be trusted, probably all of them, but I don't personally know all of them so can't say that.
Again, welcome to WoV, may you enjoy your time here.
Vultures can't be choosers.