The Bridgestone TW34 (stock rear) with a Shinko 241 up front will cover most things — although the 241 is fairly soft so it will wear more rapidly, but again, for 50 bucks it’s not that bad, and gives you excellent off road capability
The “road going” tires for the TW, are the Bridgestone TW203 and TW204 combination. There’s a pair in our classifieds as today. Bit pricey (not the ones on sale here), but hard wearing very grippy tires on tarmac
Not so hot off road as you can tell by the tread pattern, but with care, they will still get you most places
I believe Shinko does a similar tire, slightly cheaper, check fleabay for model numbers
As these “road tires” are best on tarmac when they keep their profile, you can up the tire pressures to 22psi to 25psi quite happily, which improves top speed and mpg — lower the psi to 18 or less for off road as you would expect. Running tarmac constantly at lower pressures will result in a “flat profile” on these, so carry a small pump with you
Although the TW34 rear is excellent at both on road and off, try not to mix knobblies with smoother road tires — it’s not good for the handling at all
But get rid of the stock front while you’re ahead — it’ll catch you out eventually ….