Before I start I'd just like to make you aware that I'm also learning photography so my opinion isn't going to be worth very much as i'm a newbie, but here goes.....
Personally I love wide angle lenses for landscape photography especially if you can get an interesting subject in the foreground and have wonderful scenery in the background (I've been eyeing up a Sigma 10-20mm which on an APS-C sensor (x1.5) which comes out about 15mm-30mm in 35mm equiv) For big landscape I guess you'll want lots of DOF so f8/f16 + I guess (don't go too high or you get diffraction). If you google a website called DXomark.com they review lenses and tell you the sweet spot for your lens i.e. lens blah is sharpest at 28mm f5 for example, so that might be helpful?
If you wanna get really nice sharp pics don't forget your tripod (even a travel one if space limited). And prob best to do some research i.e. what's the best time of day to go? early for a sunrise / late for a sunset for example.
If it were me I'd have a look on flickr (or equivalent) and search 'grand canyon' and see which pics you like and check out what lens and camera settings they used. I like wide angle but some landscape photographers will use tele lenses to get close to a particular part of the scenery.
I suppose if space is limited (family holiday?) then you may also just want to look at upgrading the kit lens? That said kit lenses are pretty good now days so you may end up spending lots for a small improvement in quality? Again i'm also eyeing up a tamron 17-50 f2.8 as an upgrade to my kit lens :-)
Other things to consider are filters, how about a circular polarizing filter if you're shooting in the day time to boost contrast? or maybe a 10 stop ND to do some long exposure work?
Hopefully David will be along soon to point you in the right direction, but i guess the main thing is to have fun and post your results on here :-)