Fit is critical on a bike where your hands, feet, and seat are going to be fixed for 4-10 hours every day when you're riding. REIs vary; some may have people who know how to fit a bike to you, others will say, "looks like you have enough room there, you're good to go." Run away from the latter.
As a substitute for a professional fit, people who've been riding a fair bit can test ride a bike for a bit and get a good feel for whether the bike "feels" right or not. Since you're not in this class, you probably need a good fit. Try to test ride the bikes you're interested in for 3-5 miles, minimum, anyway.
One good thing about REI is that many of them have at least two or three models of touring bikes you can try. Touring bikes are a very good idea if you're carrying the load on the bike; if you're using a trailer, it's not so critical.
Don't get hung up on carrying too much gear. You're only a day's ride away from parts with mail order and ovenight delivery. You do need to be able to repair flat tires, and it's a good idea to be able to replace a set of brake pads. For everything else, duck tape or thumb into town and pull out a credit card.