I am surprised that you are finding used four strokes cheaper than the two strokes. In my area a 10 year old 250 two stroke that is in good condition can be found for around $1500 while a decent four stroke would be $3000.
Keep in mind that dirt bikes come in several different flavors and you get what you pay for. The low end bikes are usually referred to as "dirt" or "trail" bikes while the higher end racing bikes are usually usually called "MX". The "trail" bikes will be a lot cheaper, and a lot heavier.
The pros for a "dirt bike"
Usually comes with a kick stand.
Some have headlights for night riding.
Electric Start is often a feature
lower seat height
the engines are usually more reliable, require less maintenance.
Much less expensive.
The pros of a MX bike
High performance engines (requires higher octane gas)
more travel on the suspension
Greater ground clearance
Lighter
As far as the type of riding you do, if you want to hit the MX track then I would highly recommend getting a MX bike. A good running MX bike will do just fine on the trail but a trail bike is going to suck at the track.
And "trail" means different things to different people. To some a trail is a well marked, smooth, easy path to follow. When I go ride with my club, a "trail" is something that a mountain goat has difficulty on.
When looking for a four stroke, be aware that a 230cc bike is probably the cheaper trai model while a 250 four stroke will likely be a MX model.
You might want to consider that the first bike you buy to be a temporary thing. Get a nice cheap 230cc trail bike to learn on, then plan on replacing it with a MX bike in a year or two.
Rod