Hmmm, how old are you, how tall are you, and how long have you been riding?
The 250 and smaller CC four strokes that have been mentioned are reliable chuggers, but many riders outgrow their capabilities and adding performance parts to them just doesn't give you the results in the long run (sorry if I've ruffled any feathers).
Now someone said dont' get a two stroke, and I can't exactly agree with that. There aren't many but the two strokes that are made for enduro riding are fantastic for tight trails. The KDX200 or 220 is a bit on the heavy side compared to the 125s you've ridden, but not compared to the 230s and 225s that have been mentioned here. It is a reliable, fun to ride two stroke that is already set up for the woods, with plenty of aftermarket support if/when you start wanting more.
KTM also has some sweeeeeeet enduro bikes in its lineup. The EXC models have a factory installed heavier flywheel (aftermarket flywheel weights are available, but I tried one and hated it). They also have a tall-geared 6 speed with a "granny low" first gear, plus lights, big tank, etc. The MXC models have the big tank and heavier flywheel but a close-ratio gearbox (still 6 speed though) and while they come with a lighting coil, they do not come factory with the actual lights. Easy to add if you want. A lot of used ones already have them on there. These are available in 200, 250 and 300 cc models, and the bigger ones are actually in some ways easier to ride because you can lug those guy down to a near stall without fouling a plug, provided you are jetted correctly. They are lightweight, reliable in my experience, and have "big boy" suspension which a lot of the XR, CRF-F, XT, DRZ, TTR, etc. models do not have. You can pick up used models for 2500 or less. The KDXs have sort of stabilized price wise since Kawasaki quit making them, and they have almost a cult following--for a good reason.
So, there's my sermon about two strokes. They are not the fire breathing monsters some people say. In fact, you could buy any Japanese motocross two stroke, add a flywheel weight, change the gearing, throw on some protection items and a big tank, and have a VERY capable woods bike.
But if you're determined to go four stroke, well they have their place too. I prefer a two stroke. I think they get a bad rap. It's worth test riding one of the ones I mentioned, if you can find someone who will let you try it.
One last thing: You say you are "driving through the woods with no trail at all". Unfortunately, that's illegal in a lot of places now. Recent Forest Service rule changes have made a lot of areas "closed unless posted open" which means if there is NOT a trail, with a sign telling you that motorcycles are OK, then it is closed. Charging off through the untracked forest is a no no in a lot of places. And breaking those rules is exactly what gets a lot of trails shut down, and gives dirt bikers a bad name.
But if you live somewhere that does not have such rules ... can I come visit?