My .02. It doesn't really matter what kind of tube you use. That being said, if money is no object, why not go for an Ultra Heavy-Duty? I've used them and have found they're no harder to get in the tire than a regular one. I will say, though, after using the UHD tubes once and having my rear tube explode after it was punctured by a nail, I wont' bother paying the money for them again.
I think they might be worthwhile for those who do low-psi off-roading, but that's something I never do.
I carry a spare rear tube and a spare front tube. I carry a tube patch kit, but really don't plan on ever using it. If you're going to the trouble of fixing a roadside flat, why dick around with a patch kit when you have the tube out, anyway? Might as well just put a new tube in and be done with it all at once. That's the same reason I carry one of each, although it is claimed that the front tube will work in the rear tire in a pinch. But, you can't leave it in there indefinitely, so you'll eventually have to go to all the trouble to swap it out when you get home, anyway: double the work.
That's just me, though. If I patched a tube, I wouldn't plan on leaving it in the tire indefinitely: I'd want a new tube in there soon. A couple of spare tubes don't take up much room, but the heavier tubes are harder to fold up and take up more storage space, so I would recommend standard tubes for spares.
If you've never done tubed tires, look around for an old used wheel and tire that approximates the size of the KLR rear wheel. You can use it for practice whenever you want: saves wear and tear on your good rims and practice makes perfect when it comes to changing tires and tubes. You can usually find one on eBay for less than $50: money well spent in my book.
I use an Eagle Mike Quick Jack to get either wheel off the ground but there are lots of other options for doing that, from home-made jack stands to center stands, etc.
A portable compressor such as a Slime compressor is a must-have, in my book. I'd much rather use one of those than those CO2 cylinders.
Two things I really wished I had when I fixed a roadside flat were something to put on the ground to use as a work surface under the tire (I wound up using my riding jacket) and either something to clean my hands with when I was done or some rubber gloves to wear while doing the work.
You can use the Search function on here to find threads with opinions about inner tubes, changing tubed tires, etc.
Flat tires don't really seem to be all that common, but it's nice to have the stuff with you to fix one and then continue on your way if it does happen.