For grips, it is a preference thing... Some like softer grips, some like firm. Size of the grips can vary - and generally I would recommend you use a normal grip size unless you have oven mitts as hands. Then maybe go with a medium sized grip if you truly have large hands? Going with an over-sized grip on an iron just seems silly to me...
Weather conditions should be considered... If you play in humid to wet conditions, the tackiness of the grip will be more important than a dry climate. And if your hands sweat a lot, you may want to take things like that into consideration when you select a grip.
As for specific driver grips... A lot of manufacturers are coming out with light weight grips... I actually installed the WinnLite grips on my clubs this past Fall when I picked up my MP-59's and went with them due that they were a mere 25g per grip. And they felt soft and tacky to my hand.
For putters, the trend seems to be over-sized grips from companies like Winn and Tigershark as they help eliminate use of your wrist - and get more of a true pendulum type of stroke.
Companies like Golf Pride, Winn, Iomic and Lamkin are pretty popular. Go to their websites and look around... Then go to a local golf shop like Golf Galaxy and see what feels best to you.
I just picked up my Vokey SM4's a few weeks back, and they have a different grip than the WinnLite's I added to my MP-59's. The grips on the Vokeys feel like they are going to rip the skin off my hand as they are more like a Golf Pride Tour Velvet type of grip. Some people love those type of grips, but my preference is for a softer feel. And I'll be re-gripping these wedges soon.