I don't think that I can stop at three..
As above, I think how you plan to ride dictates the order of importance.
One of the selling points of the KLR over the DR 650 to me was that it already came with a skid plate and hand guards. Granted, they aren't super robust, but you don't have to shell out money on Day 1 if you want to do some light off roading.
That being said, I knew that I'd be finding dirt and gravel as soon as I got my "sea legs" on the bike. So before I even took delivery I had the dealership install SW Moto crash guards and skid plate.
A suspension upgrade was on my list, but once I learned that the 2015 and on models had beefier suspensions from the factory than did earlier models, I didn't see the immediate need.
I added heated grips, Bark Busters, off road foot pegs and a longer shift lever 2-3 days after bringing it home. 800 miles on and I had done the Doo, T-Bob, and KLR dash (upper and lower).
I plan on replacing the stock wind screen and adding a rear master cylinder cover and a headlight protector in a few weeks. If my riding improves to the point where I'm taxing the suspension, I'll upgrade that as well.
Beyond that, no plans other than changing the oil, chain, and tires when needed. But I do like the PVC pipe mod suggested above....so maybe I'll reconsider. LOL.