Hello
We recently arrived on a Sunday around 10:30AM local time. Once off the plane it was a short walk to immigration and about 10 min to clear. All in all, we were about 35-40 min inside the airport. If you only have carry on bags, it can be quicker. 
We had some friends arrive on a Saturday,12-2pm, and from my understanding what took us 10 min on Sunday, took them 2.5 hours plus. The line was never ending from what they said. Just think Disney world, waiting in line for a very popular ride during peak time/season..you get the idea 
 As for the ride to the resort, it is a short 20Km or 12 miles to Desire RM. Along the way you will pass a Starbucks, and a few other stores. Just in case you decide to ask the driver to stop to pick up say...a few Red Bulls or maybe a Starbucks Frappuccino..lol
As to who to use fora shuttle, well we used USA transfer this trip with no issues. Cost us $60 US or $75 Cdn for a return trip. You can pay the driver in person if you like, again in US or Canadian. There is a link on this site for them you can use as well, and it helps support the forum. 
Our return trip we departed the resort on a Monday late afternoon. From Desire doors to waiting at the gate at the airport, was all of 40 min. This has been the case as well on our last 3 trips. Needless to say, departing the resort 3 hours before flight time as they like to do...well..you will be sitting and shopping lots at the terminal. Just something to consider when setting up your return pick up time.  Depending on your flight/destination/airline, for us 2 hours if more then enough time. 
Last and a bit off topic, as for transportation once at the resort you have a few options as well. You can rent a car, 
ABOUT $130 US, but not sure... depending the car. They have small to Range Rover Evoque Compact SUVs. 
You can as well take a cab. Below is a pic of the set rates FROM the resort. 

Have a great weekend,
Cheers, 
