Hi there, depending where you live, a dual sport/enduro is a great way to start. 250 - 400cc is plenty and you're never limited to just asphalt. If you're in the city 24/7, there are great versions called motards, which are basically dirt bikes with small street tires. Depending on budget, KTM and Husqvarna are best with Yamaha and Suzuki etc making excellent models too. I just love the option of being able to leave the road and explore what isn't paved.
If you're not into dirt bikes, cafe racers are great too. They're light, nimble and they've been around forever. They might just be a little bit cool.. Ha ha. Used models galore of both!
I sure hope that helps.
Happy and safe riding!