A few things in defence of 2-strokes...
From my understanding (and I've never been on one), the 2-stroke 250's you can buy are primarily designed as race/track bikes, this means that they tend to be higher maintenance, quite powerful, and peaky (the power arrives all at once). A lot of fun, if you are into that sort of thing, but suboptimal for learning to ride.
Most of the 2-stroke 150's you can buy were designed (at least my KRR was) as commuting bikes for Southeast Asia. They aren't as highly-strung as the 250's, meaning less maintenance, and more even power delivery. They have a moderate amount of power, but you have to go looking for it, if you want it to be fairly sedate, it will be. I was a pretty timid learner, and I never had the KRR get out of hand. Reliability-wise I did have engine trouble with it, due to it running out of oil at some point in it's past. I suspect a 4-stroke run without oil wouldn't have fared much better (or been any cheaper to fix).
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