A few thoughts
I've stayed at that Best Western. Nice enough place, but a bit worn around the edges. I wouldn't hesitate to stay there for a night, but if you are the kind of person who goes searching for chipped tiles in the bathroom, it might not be the place for you. (EDIT - reading this, it sounds a bit harsh - the place is clean, just not new).
If you decide you do want a Best Western-type of place, let me throw a few additional options at you - the Airport Doubletree is very nice - but not quite as close to the airport and is the opposite direction of the strip. Second would be the Holiday Inn Express South - great place I stayed on my last trip. Great room, fine breakfast, close to the strip (there's a free shuttle to the strip, though it doesn't run all that frequently). Wherever you stay, you want to check the times for the shuttles - some stop running at 10:00 or 11:00, which will be tight for you.
There are a few problems with staying in a casino-resort hotel that night. First, many won't take a Saturday check-in, and the ones that do are probably going to be expensive. Second, the casino resorts are huge, and checking-in is going to take a lot longer than at a Best Western type of place. Third, Best Western-type resorts are going to give you a free breakfast, which can save a lot of time and hassle. And none of the strip resorts will have an airport shuttle.
On the other hand, the casino resorts are right there on the strip, and make for good sightseeing.
Best of luck,
Zeke