Curt said:
Lots of people (including ZooTech above) will tell you to get a big bike. Don't listen to them. They will tell you that you will get bored. I think that depends on you more than on them. Some people always want more. Since you're looking at the 250 and the 125, I'll bet you're not one of those people.
Curt
I'd hardly consider a 500cc motorcycle "big". In fact, I think with the release of the Vulcan 2000, the VTX 1800, the Warrior, and the new Triumph, eBay will have to re-think their categorization method of >700cc = large.
A 500 would have been considered "big" in the 70's, when a lot of people were riding Honda 350's around. Nowadays, a 500cc is definately a small beginner bike, and a 250cc motorcycle is something you fold up and stick in your backpack.
I started out on a 500cc Honda, moved up to a 700cc 4-cylinder (80HP/50ft.lbs. torque), and now have my Mean Streak (700+ lbs.). I'm here to tell ya, a nice early 90's Yamaha Fazer or an Interceptor would be a fine machine to learn on. Bikes like that handle well, brake well, and are easy to find parts for. You'll be better off spending $3k on a 10-year-old used 500+ cc four cylinder than on a brand new 250cc scooter. I'm tellin' you because my two best friends and I all started out of 500's (a GL500i and a CX500) and by the end of the riding season all we could talk about was what bikes we were going to replace them with come Spring. Now I ride a Mean Streak (after stepping up to the aforementioned Nighthawk 700SC), my best friend is on a Harley Sportster 883 (and will be rebuilding the engine to 1200 spec this winter), and my other friend is thinking of trading the GL500i (that my other friend sold him when he got his Sportster) for a Suzuki M50, S83, or Yamaha Warrior (depending on his finances come Spring).
If you want to blow $2500-3000 on an Eliminator or Ninja 250, by all means go ahead...it's your money.
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It'd be nice to know how old you are, how tall you are, and how much you weigh.
Me, I'm 27 years old, 5'10", and about 210lbs. I once rode a Nighthawk 250, and it felt like a glorified moped. It certainly wasn't anything I'd be crazy enough to enter a freeway with.
Personally, I think a good rule of thumb to go by is to look for a bike that weighs at least twice as much as you. For me, that would rule out anything in the 250 class and immediately force me to look at bikes like the Suzuki SV650 or V-Strom. I suppose if you're a lightweight, perhaps a Ninja 250 may be a decent first bike....but I'd pay close attention to semis on the freeway and would pass with caution. My mom (5'4" ~115lbs) got blown over by a semi while riding a Honda Rebel 450, and subsequently did a 75mph Superman (err....Woman) across three lanes of freeway where she ended up in a ditch, essentially okay except for a concussion and some gravel in her elbow. That is why I recommend a late 80's or early 90's UJM (Universal Japanese Motorcycle) for a beginner, regardless of engine size (but at least a 500) since they're usually easy to repair, easy to find parts for (eBay) and generally have some decent heft to them because of their steel frames.
Folks here think they're doing you a huge favor by recommending a 250 since you're a beginner. But if you're that much of a newbie, you need to avoid the road all together and go learn how to ride on a nice used 4-stroke dirtbike (maybe even an enduro, so you could enter the road when the time is right). That way if you fall over, you'll land in some nice soft dirt and maybe bend some $20 handlebars at worst. Once you've got the balancing/clutching/leaning/shifting thing down, a 500cc streetbike will be a piece of cake. I'm tellin' ya, unless you're like 5'6" and weigh 150lbs or less, you'll kick yourself for buying a 250, and you'll want to throw a 125 into a lake.