Late April through May is a wonderful time in the Sierra. It will definitely still be winter, but the snow will be well consolidated. Keep snowshoes in the back of your minds, but it is likely that you can leave them behind; watch this board when the time gets close. Even during the dead of winter, with some deep powder conditions after every storm, snowshoes are almost never needed above 12,500'.
Snow depth this year is about average, perhaps a little on the low side down Whitney way. There is never much avalanche danger if you travel the main trail – only two spots where you have to be careful, and those only immediately after a serious storm.
I don’t know about renting stuff; others can respond on that. Plastic boots would be nice, but good waterproofed leather ones are just fine. (I made many an enjoyable winter climb of Mt. Whitney before plastic came on the scene) Just make sure they are large enough for a good sock complement, and use substantial gaiters. You’ll definitely need crampons and ice axes.
There's a lot of good data around on acclimatization to these elevations, and ways to accomplish it or overcome the lack of it. If you do the right things (stay hydrated, limit yourselves to 2500 feet or so per day, maybe take along some chemicals, etc.) you'll do fine.
There are two excellent guidebooks, one by Doug Thompson, who is the moderator of this board (Mount Whitney: Mountain Lore from the Whitney Store, 2002) and one by Paul Richins, Jr. (Mount Whitney: The Complete Trailhead-to-Summit Hiking Guide, 2001). There are others, but for thoroughness you can’t beat these two. Both available on Amazon.com if you can't get them locally.
Having climbed Mt. Washington (it was stormy that day, naturally), I know why you are asking about cairns! But don't be concerned. They are neither needed nor present on Mt. Whitney. The Sierras are one of the most pleasant ranges around for predictable and benevolent weather conditions.