Wrap That Rascal
Did I protect the albums that I bought as a teen with outer sleeves? No. Do I wish that I had? Yes. Like every other opinion given on this site, one size will never fit all. Do what works for you and your budget. Now that we got that out of the way...
What are the benefits of protecting your albums with outer sleeves? While some say that outer sleeves will protect your album from collecting dust, the purchase of a good inner sleeve is going to do a better job of protecting your wax than the outer ever will. If your budget will only allow the purchase of one, I would recommend replacing the factory inner sleeve. That's an entirely separate entry though, back to discussing outer sleeves.
I've moved a lot over the years. When I didn't have my albums protected by outer sleeves, they'd take a beating on moving trucks. Regardless of how well you pack them, they're bound to slide around in the milk crates or boxes you pack them in. Movers will also stack your albums on top of other albums even when you specifically tell them not to. Outer sleeves have really helped over the years where this is concerned. Bottom line: if you enjoy pristine covers like I do, outer sleeves are going to eliminate the scuffs and scratches that will accumulate over time. You're going to eliminate any discoloration that's bound to occur as well.
I've found that spending a little extra and picking up outer sleeves that are at least 3 mil will be a better bang for your buck over time. You won't have to deal with them tearing or wrinkling as much as you will with thinner sleeves. I'm not sure what your local record store offers, so I'm going to suggest what I purchase from Amazon. They're 12.5 x 12.75" so you have extra remove for your double albums and won't tear the seam of the sleeve attempting to slide them over your album like you will with something offering smaller dimensions.