We LOVE Vegas. It's super fun and exciting.
We have scored some great deals with Expedia for airfare and hotel, sometimes we have gotten a car included or not and rented on our own. DH gets a really good company rate so we normally go this route when we are going to rent a car.
Each Resort has a theme and something to check out, so I would start by seeing what interest you. For your 1st trip stay on the strip. Do be aware that a resort fee will be applied above what you pay up front, get a players cards and use it. Call before check out and see if you can get the resort fee comp'ed, it's based on play, so both of you get the card.
Watch the cab ride form the airport, no tunnel.. cost more.
There are 2 tickets stands on the strip( one at each end I know that there is one across the street from the Mirage its next to Denny's), that sell reduce price tickets for that day. Be there early ( when they open for best selection), and make sure you have a few choices of shows you would like to see.
Food Cost - be prepared, if you think WDW is expensive get ready. Check out your favorite chains and look for them on the strip they are there do your homework so you know where they are ahead of time. All the resort will have food courts, while it's fast food, it is still a higher cost than what you pay at home, not to much.
Freemont Street, Old Las Vegas, is worth a trip, It has a whole different feel to it. It's cool walking thru it, you can feel the sense of the Rat pack, Elvis, and other performers of that era. You do want to be super careful down there, late night it's gets a bit seedy. There are some good deals for buffet and meals down there so check it out.
There is public transportation, during the day we find it okay. But late a night not so much. Drunk people throwing up on a bus is not fun for anyone.. happened to us, late night worth the $$ taxi ride...
There are a ton of street performers, be cautious.. nothing is free in Vegas.
As far a clothing, the casinos are freezing, and I am hot all the time, and I have to wear a sweater or hoodie while playing. It does get cold at night so pack accordingly.
When heading off the strip, Grand Canyon on the Indian Reservation side is the closest and most natural, and they have the sky bridge, its about 2 1/2 hours or so away, on the other rim its about 4 to 5 hours drive one way. We prefer the Indian Reservation side, we love the natural feeling, last time we were lucky enough to see a wild coyote.
Red Rock's is another good place to check out. Its a big car loop with lots of spots to get out and check out the lay of the land. Also I think that they offer horse back riding near there.
Vegas is super fun, but keep your eyes open and beware of your surroundings... After all its 'Sin City" for a reason.