go national cars, join their club (you can have the fee waived, just google it), then you can rent a 7 passenger van and pay only "mid size" car prices, and no need to line up at the counter, just go to the car and drive away. makes a BIG difference. usually a van can cost you over hundreds, depends on how long your stay is. also, book ahead, save you tons.
New LYK is not user friendly and is annoying. Now you can blow me.
Make sure you check the final total on your quote, and not just the per day rate. Usually picking up car at the airport, or popular location, there is a special "Premium Location" surcharge, which can be quite a big chunk of money.
Also, check if your credit card and your car insurance have coverage on rental. If so, then you can save on CDW. Just beware that, if you do have an accident (touch wood), some credit card company may need you to pay for the damage first and then submit a claim.
I also like National, as they allow you to pick your own car from the lot.
I bidded my car at Priceline and got a compact rental for $13/day. Eventually I got my rental at Budget. You could also have a look at Hotwire Hot-Rate, those are limited time offer. You just have to check around for best rate.
In Vegas, their car rental is at another seperate building. There will be shuttle bus that will drive you there for free from the airport. Once you are there, you will be walking into a very big facility in front of a huge parkade. Simply follow the sign to find your rental company and the lot attendent will show you your car after all the paperwork.
Generally avoid the cheap ones like Fox, Payless, Advantage because I've heard bad stories with them. If you go on Priceline or hotwire, they only give you the big ones like Hertz, National, Budget, Dollar and Enterprise.
Before you leave the lot, please inspect the car carefully for dents and obvious scratches, bring a flash light with you as the parkade could be dark to show the scratches. You will need to give the paperwork to the parkade exit attendent and you will leave the facility.
Mini-van obviously will be more... you plan to go to Grand Canyon?
Since GPS is a $10 option for most, if you have one that is updated, bring one with you as you will probably want to know where is Walmart to make your first "beverage/snack" stock up.
From my understanding, if you got roadside plus from ICBC, you got rental insurance coverage which is good for car rental in North America, but not sure about the details.
Last time when I decided to go to Grand Canyon, I was thinking to rent a car but end up join the tour. The drive is like 4-5 hours from the strip one way plus the highway is completely dark...
It would be a very tiring drive. So I am glad that I actually join the tour instead of driving. But I guess if you go with more people then worth to drive.