Short answer in three words: Whirlpool, Whirlpool, Whirlpool.
Longer answer: Odds are that any refrigerator you buy nowadays will not give you as many years of trouble-free use as they used to. What I want is a good, faithful, well made appliance that gives me the best odds of not needing repair, and most importantly is made in a way that facilitates easy, inexpensive repair when something does go wrong. Any independent repair person can repair your Whirlpool, if something goes wrong, and you have the best probability of it being relatively inexpensive, compared to other brands. Just don't even look at GE or Frigidaire.
Whirlpool also makes Roper (plain, smaller, bargain basement) and Kitchen Aid (more expensive).
Kenmore doesn't make appliances, but they sell appliances made by others, like Whirlpool (good) and GE (not). However, one problem I have become aware of when buying a Kenmore, even if it is really made by Whirlpool, is this: who are you going to get to do service if it needs repair under warranty. I have read many horror stories of people who go through a lot of hassle to get Sears (or the company they hand it off to) to fix their appliance under warranty. This is not the way Sears used to be a decade or so ago.
I would browse appliance repair forums to see what you find.
For buying, you can see what Whirlpool has on their web page, along with their list price, then shop online at Lowe's and your closest appliance superstore.