I can't really agree with what's being said here.
I started flying out of VGT (North Las Vegas) with very limited experience more than 20 years ago and have been back there every year since. To address the specific points:
Aircraft performance: The answer to this is go solo. Even a 152 will go to the Canyon 1 up and cross the VFR routes. A 172 2 up and little baggage will do the same.
Bumps, hot n high, etc: Fly early. A great benefit is to stay close to UK time. Take off at 6am and be done by 11. Also good for avoiding summer thunderstorms. Most places open by 6am and you can get the keys if you want to go earlier.
Desert terrain etc: Yes it's challenging if you have to walk out. But in most other respects it's a far easier environment than UK. Stay away from the lee side of the mountains on windy days and that's about it. (Less wind in the morning). Don't go exploring canyons etc or deviating far from planned routes. Use flight following - a LARS that works - and you've got a guardian angel. Use height - 5000' agl - enroute.
Airspace: a pussycat compared with UK. Clearly defined consistent airspace with vast areas of uncontrolled in between. No problem with joining class D and only simple proceedures for 'B'. If you want to fly into 'B' at Vegas it's probably best to check out there first. But compared with Cardiff/Bristol/ London megaport it's a doddle.
Checkout (re above): Check rides are a gift in the American system. Some places have minimum experience requirements but many don't. A typical checkout is the same as a BFR, 1Hr gnd and 1Hr flight. But if they want you to have 5Hr, do it. Make sure they cover enroute proceedures, flight plans and radio. Most US instructors have no idea how rudimentary things are here and that many of our PPL's are unsure of the radio. Buy the little book 'VFR radio proceedures in the USA'. They don't appreciate we don't even have flight following or even a VFR flight plan system that works.
Briefing: The 1-800-wx-brief system is another gift. Be sure to use it wisely. Call the night before to discuss your plan. They are reluctant nowadays to give out stuff like car rental reservation numbers but in most other respects the new privatised FSS agents are the same people as before and just as helpful. Call again before departure to discuss current weather and TFR's. Stick to the route that you give them.
GPS: If you can, rent a plane with a panel mount GPS and learn how to do 'goto'. Failing that, take a simple hand GPS with Americas data like the Garmin 92. Navigate off the excellent sectional chart (you arethere to see the landscape!) but verify your navigation with the GPS so you never have any 'uncertain of position' nonsense. Sectionals are cheap, convenient (fold up easily) and can be supplimented by WAC charts for longer trips.
Weather: If your'e not sure, don't fly. It's a big country and you can get into big trouble. Having said that, it's far easier than UK with its micro weather and c**p forecasts. Just wait until tomorrow. They can see the weather coming days in advance.
Where: VGT Westair as has been said or Northaire at Prescott, only an hour from the Canyon and no airspace other than 'D'.
Sorry to write at such length.
Good luck - you'll never regret it.