I think you might want to change the suspension out on it. I think that'd be about 500 (rear)+100 (front).
Your height is a good thing with the KLR - it is a tall bike. I'm 6-4 and it fits me like a glove.
The KLR is a good bike for your intentions - street, back roads, fire roads, trails ect. The KLR runs into problems on the heavier off road stuff...it is just too heavy to be easy to manage.
But before you do anything, I'd give the bike a whirl to assess your need for 600 dollars in suspension upgrades.
As for the klr's 'make' and 'model', there are two major ones. Generation 1 (1987-2007) and Generation 2 (2008-present). For the most part the differences between the two models is cosmetic.
I am not sure if you are aware, but the 'doohickey' is a part prone to failure, specifically on the generation 1 bikes. It can literally break, leaving metal fragments circulating around in your engine case. Its about 100-150 dollars to swap out with a quality aftermarket piece. It is possible the previous owner has already done it, so you may not need to worry.