I've rafted the Canyon ten times, and cannot recommend it too highly. I would strongly suggest an oar boat trip for the longest duration possible (probably 14 days). If you can't manage the time or money for the whole thing, I'd say the lower half has the better hiking, though the upper certainly isn't at all bad.
As for companies, I can certainly recommend Arizona Raft Adventures (AzRA). I'm sure plenty of others are good as well, standards are generally pretty competitive down there, but they're the ones I have personal experience with. Excellent guides, good food. I think they even offer hiker special trips.
One more thing to consider is what season to go. The summer months have more water in the river (so the river miles go fast) and longer daylight hours, and hence more time for hiking. The hot weather (very hot indeed!) also makes the many wet hikes and swimming opportunities much more appealing, not to mention the whitewater. On the other hand, monsoon season (July and August) can keep you out of certain side canyons due to flash flood danger. Spring and fall have fewer people on the river, and the cooler temperatures open up a lot of dry hikes you could never even contemplate in summer. The green grass, flowers and blooming redbuds and ocotillos in spring are really nice. Overall, though, I'd say June to early July probably gives the best overall experience if you've never been before.
Whenever you go, it'll be an amazing trip. Rafting the Grand is everything people say it is!