Bridgestone Grittys are good and worth the extra dosh, Mitas EF-08 are cheaper and good for the money.
Gritty's on the front and a Mitas C-02 on the back is a very recomened and well known choice. I have mitas (non-leagal but modified for MOT shhhsh!) front and rear on my klx and it seems fine but Grittys do clean up better if it gets sticky.
Stick with the NHS till MOT time. They are OK on the road and the dogs bollox off. I have a B F Goodrich Crossengos on the rear and that seems ok and has a E on the wall so is road legal.
How do you like the KLX? I have a 250 and have been well pleased with it so far.