If you are a hotel guest they have a free airport shuttle...
...Not sure about public transit from the airport to Summerlin, but my guess is it is a huge hassle. There are also shared limosine services such as Belltran that are reasonably inexpensive. A rental car in Vegas is, in most cases, the best as well as least expensive choice if you're planning on casino hopping off-Strip.
The only casino close to the SunCoast is the Rampart, about 3/4 of a mile away, right down the street.
The public transit option is the airport express, which obviously starts at the airport and ends at suncoast, via downtown. The trip is mostly highway. It does not stop at the strip, except to cross at tropicana. The cost is $2 and takes about 45 minutes.