I have a KTM 500 EXC-F. It comes from the dealer in street legal trim with a license plate for all 50 states.

The size of the engine doesn't necessarily indicate how much power a bike has as you may be aware from your experience with street bikes. A Honda CRF 300L is much more tame than a KTM 350 EXC-F even though they have similar engine sizes (think about the power difference between a 1000cc crotch rocket and a cruiser which might have a 1200cc engine that makes significantly less power).

The KTM 500 has more power than I can realistically use in the dirt but I like having that much power available for when I on the street. It can easily cruise at 75-80mph and can go triple digits if needed while my wife's Honda CRF 300L tops out around 70-75mph.

The trade offs between the KTM and the Honda are performance, price, and maintenance. The KTM makes about double the horsepower of the Honda and weighs about 70lbs less. The KTM cost about double what the Honda cost. I change my oil every 500ish miles on the KTM while her oil changes are every 8000 miles.

The 300L or an older 250L will be a great starter bike but you might wish it was a little lighter on the trails and that it had a bit more power on the road.

Other street legal options off the top of my head:

Kawasaki KLX 300 Suzuki DRZ-400 Yamaha WR250R

There are certainty other options as well (KLR650, DR650, etc but they're heavy) and there are also ADV bikes which can go off road if you can handle the weight.

I've raced motocross and also raced woods events and also do a lot of other off road riding on quads and UTVs. As the guy before me said, CC size isn't always going to directly reflect power. A crf450L has a 450 race bike engine and has much much more power than say a DRZ 400. I would suggest going with a CRF 300L. It will have enough power to handle almost all trails outside of steep steep inclines. It's a great bike and doesn't require much maintenance and is relatively inexpensive. Also couldn't go wrong with the DRZ 400 but I think it might be a little heavier and slightly less capable. When riding off road, too much power is often a hindrance rather than help. You can often go faster in the woods on a 250 race bike compared to a 450 because it is lighter and you are not having to fight the power output of the bike as much. A 250 4-stroke or 125 2-stroke bike would be a good option for starting as well, but they aren't typically set up for registering for road riding.

Good luck if you decide to get a bike. Take it slow at first, off road riding is much harder than road riding and there are a lot of lessons to learn that are best not learned the hard way. ATGATT