Its only going to be for a short time, so go with something reliable, that has a decent following (for resale value), regardless of size. When you get your full license, you will upgrade any way. If your concerned about size because of your height, I'm also 6'5", and there aren't a lot of bikes out there that will feel or look correctly sized, even once you qualify for unrestricted, so a compromise is necessary. I started out on a 1997 Honda XR250R, It was a great all round road/trail machine. I think dirtbikes give way more bang for their buck in the LAMS department, and are easier to re-configure to your height than a road/sportsbike. They go anywhere, are cheap to run and you get the best of both worlds. You can trick them out nicely too, if thats your thing. I currently ride a 2011 DR-650SE, It's a solid reliable workhorse, LAMS approved, plenty of info available in the mods/upgrades area, and it fits me great. It (like the KLR650) runs really well on the highway, and around town as a commuter, cheap to buy new (under $7500.00 on road) and will last you till your on your full license.
The main thing to remember is that motorcycling on your L's & P's can be some of the best and most fun times you can have on two wheels, I have had many great times on some great and powerful motorcycles, but some of my best memories are from when I was restricted to my trusty old XR250. It becomes an addiction, and soon enough you will long for more and more power, but there is beauty in the simplicity and utilitarian nature of a small bike.
just think, Hi-rise handlebars and riser kit, Lowered footpegs and extra foam in your seat, heavyweight rear shock spring with the right pre-load and you'll be comfy as.
And if you end up going with a sportsbike like the tried and true CBR250RR, you'll have no probs getting your knee down in the twisty bits, and just think like Bowser in MarioKart!