If you want to spend more, the new 400 has even more improvements. It's got a shorter wheelbase to make it even more agile, and quite a bit more power (70% more horsepower and 82% more torque than the NewGen 250). You're probably going to spend a couple grand more on a 400 than a 250, but you are getting a significantly newer bike, with fuel injection and a lot of bells and whistles. The 400 seems to have plenty of power on tap at all times, whereas people have said that they need to plan passes a bit more and things like that on the 250, due to being a little low in power. The 250 is still a highway-capable machine, just don't expect it to always have rocketship power with a flick of the wrist. The 300 falls in between, basically being a 250 with a slightly bigger engine and FI.
I'm 6'1" and currently around 240, and the 400's suspension feels pretty good. I'd like to get springs matched to my weight, but there isn't a ton of data on spring rates out there (to where I feel comfortable just ordering some new ones). My '09 EX500 had even softer springs than the 250, and upgrading those was the single best mod (out of a bunch, some quite expensive) that I did. The EX400 is miles ahead of that, stock for stock.
You can play with
http://cycle-ergo.com/ to get an idea of how you'll be positioned on a specific bike. The little Ninjas look like their big brothers, but they're more of a standard, upright position than the ZX and CBR-RR models, which are basically race bikes that have had the street-legal bits added on. You're not hunched over hugging the tank like on a race bike. There is a bit of a forward lean, and you'll need to learn to use your core to support your weight (as opposed to leaning on your wrists), but these little Ninjas aren't too bad.