A ninja250 is a good beginner bike, fun and forgiving. Sometimes on the freeway you wish for more power; it's nice to be able to escape situations by fleeing quickly, you might want to consider a ninja500. However, that said, I was happy with my ninja250 as a first bike.
At the end of the MSF class you take the same test that would be administered by the DMV. However, note that the brunt of the riding in the class is spent practicing the exact same exercises as are in the test, so you should be able to pass it. You almost certainly won't pass it if you take it at the DMV without significant practice of those exercises.
The DMV thing depends on the state. I lived in AZ recently, and there was a beginners course that left you with a MC endorsement on your license, saving the nasty DMV experience. I don't think that's true in every state, however. You are going to get a ton of advice on a first bike-- I would ordinarily recommend a dual-purpose bike, though 2 hours on the freeway on a dirtbike could be kind of brutal. A used Suzuki GS500 or Kawasaki 500 ninja would be good. The 250 might be a little buzzy and uncomfortable for cruising down the freeway for two hours. For insurance reasons, plus the fact that you will likely have a tip-over or two, I would definitely recommend against a new bike at first. Get a good cheap used one, thrash it for a year, then make the decision about what you want for the long term. Go to www.cycletrader.com and browse around for used bikes in your zip code.
The ninja 250 or ninja 500 is a good bike to start on. The suzuki GS500 is also a great starter bike. You might also want to start on an enduro (e.g. DR200). If you had fun on the Honda dirtbike, an enduro is a very easy/inexpensive way to learn and won't suffer as much damage if you have a few beginner incidents.
The 250 is great but see how well you fit on it vs. the Ninja 500 and 650. I'd lean toward the 650 but then that brings the Suzuki SV650 into the picture and the Moto Guzzi Breva 750 and Triumph Scrambler. Get to a bunch of shops and take a seat. You are new enough that everything will seem like the best thing. Keep riding that dirt bike too.
re read SR's comments about 172 more times! Keep riding that dirt bike. That will make you a MUCH better street rider.
A couple mentioned checking if you fit the Ninja 250....yes, by all means.
And if you fit, what a nice starter bike. Lots of them out there used with very low miles.
My brother finally took the course (sorry, no info on that part of your question) and bought a lighly used 250. He is about 5'9" & ~200'ish. He fits just fine. Bro has about one year on the 250 and is ready for the next step up. Karnak see Wee Strom in the bro's family by next season.
I'd go Dual Sport these days. DRZ400, DR650, KLR650/250, or if you like the gee-wiz factor I believe Husky makes some real nice machines. The Dual Sports are real easy to ride can do gravel, dirt, or pavement and they cheap to buy and insurance is low.
Check your state's requirements. In Washington if you get your learner's permit from the Department of Licensing (DOL)you must take their silly little parking lot test despite completing the MSF course. If you start with the MSF then DOL will simply issue your (all motorcycle) endorsement when you show them your MSF certificate.
The little Ninja is not only a good beginner bike, it's just a good bike. I seem to buy another one every few years just to ride for giggles, but the 250 does help you learn to ride smoothly and with foresight. There is a lot more to being a good sport bike rider than having quick wrists and hands. The Breva 750 is a great bike, specifically designed for beginners or returning riders--I've always referred to it as the Miata of motorcycles. If you live where you can ride a dirt bike make sure you try it. like everyone else said its a really good first step.
Never ever ride with somebody who's horsepower exceeds their IQ