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For $1k, you're going to be hard pressed to get a decent all-around bike.
$2k is doable, you can find used KLR's and smaller dirt bikes for that price.
For dualsport use, if you're on the road for anything longer than 15mins, get a four-stroke. Especially if you want to do longer rides, nice to swing into town and top off at the pump without having to mix oil. 4's are a lot happier on the highway anyways.
For the 1-2k price range, take a look at an XR. Higher elevations (>5k ft) you'll want a little more displacement, lose a lot of power with the lack of oxygen. Sea-level, a 200/250 would be enough.
Wide-ratio transmission for woods and DS use. Makes the ride a lot more enjoyable when you buy a bike designed for the application.
Don't buy a MX/race bike. It can do trails/roads, but you're going to be doing maintenance on it after every ride.
Honda XR, Yammy WR, or a Suzuki DRZ are my suggestions.
Getting it plated/street-legal depends a lot on where you are, check with your local DMV about what needs to be done if you want to go that route. I recommend it - that's the best money i've ever put into mine.
Factor in gear too, if you don't already have it. Decent boots (ankle support, good sole), moto jacket with shoulder/elbow/spine armor, gloves, and a helmet. You can burn through your budget pretty quick on gear alone.
Pic related, tonight's ride. '07 KTM 525 XC-W. Quick 60 miles around town, few miles of winding 10m/h-speed-limit mountain gravel roads, to 75m/h interstate highway.