Take a taxi (cab) which will run you around $15.00, or take one of the airport shuttles, a flat $7.50 one way which is the better deal for one person. Either way your luggage will be loaded and unloaded by the driver. Both are lined up waiting outside of baggage claim.
The advantage of taxi is that they head out immediately from the airport when you get in. The disadvantage is that you can't be certain how much it will cost. Heavy traffic (afternoons) can make the final fare higher.
The shuttles wait until at least mostly filled (8-12 people), which could be anywhere from 2-15 minutes, if that bothers you. But no matter how long it takes to get you to Cosmo, you have already paid the $7.50 so no worries there.
There are several shuttle companies with their people beckoning you over. One is as good as the other. You purchase your ticket at the stand, stating which hotel you are going to, and they direct you to a shuttle taking people to Strip hotels. The driver loads your luggage in the back.
The taxi and shuttle both pull up to the hotel. There is no off property "stop". One nice thing about the shuttle is you get a bit of a look at many of the Strip hotels as the driver drops each customer off. Kinda fun.
You can buy a round trip ticket for the shuttle but I don't recommend it because they aren't that accurate with their pick up times. Plan to take a taxi back to the airport. And, for some reason, the taxi ride back to the airport is usually without the run-around problems people often experience from airport to hotel.
Good luck and enjoy your visit!
