My pet theory is that each motorcycle has a use or personality, and after riding it for a while your behaviour ends up matching the personality of the bike.
BMW tourers make you want to ride the curves from coast to coast, but do so safely. They don't mind a bit of speed, but are also content to cruise at legal limits.
Harleys want you to cruise the straight desolate highways, without a helmet (dumb, but if you are going to ride without a helmet, the a straight desolate highway is the place to do it). They also like being polished and sitting in front of cafes.
A trail bike wants you to turn left up that hill, and go explore, while a top end enduro bike wants you to do that a bit too quickly. A KTM adventure (I have one) wants you to load it up and blast across a desert, and does so remarkably well.
Sports bikes, and the Ninja is the worst no matter what the size, want you to crouch down and go as fast as possible. They eat away at your soul, and you just have to go faster and faster. There's a bad ending waiting for you, especially for early career riders.
So buy a bike that matches your use case.
The upright road/trail bike with a top box is an excellent all-round choice for commuting, adventure and a bit of safe speed. (Triumph Tiger, BMW F800GS/F65GS, BMWR1200GS, Yamaha XT etc). A sport bike is great if you are able to use it on a track, or for the occasional blast in the desolate hills. A laid back cruiser needs wide open spaces and lots of cafes - they are not about safe speed or twisties.
But the ultimate use for a bike is travel, and the further the better. Get something you are comfortable on for hours, and which has the ability to go on anywhere.
That said, I now ride an MV Agusta F4 Brutale, which seems to offer sport bike performance without the soul eating. There's never, ever, an urge to ride wheelies downtown to show off your uber Ninja neon green decals.
Personally, I don't like dual-purpose bikes. I think they're too tall, and I never have need nor desire to go off-road in the least; for me, sport-touring is optimal. I think dual-purpose bikes are a bit like urban 4x4s: most never go off-road, and when they do, they're not actually very good at it. But of course this is a personal preference.
Dual purpose bikes are indeed harder to approach - the 1200GS Adventure I own is a huge tall and bulky machine. It took me a long time to get into them, and I started out with the smaller 650 GS series. They are however remarkably easy to ride, and to do so in almost any condition. They make great commuter bikes as you are much higher and generally have great luggage capacity and robustness for the occasional spill. However you are essentially right - they are not as good as a pure-purpose bike for a particular application. You can dial in your degree of off and on roadability. KTM does the best hard core adventure series, while take your pick for the soft roaders of dubious merit. If you do get into it then BMW run excellent (though rare) off road courses. We all had our bikes, mine a 1200GS, fully airborne on several occasion on my course. And there's a really scary photo from that same course on my eponymous blog header.
As for me, I'd recommend a tiny 250cc or even 125cc for a starter. A year or two later, you can always get a bigger one safely.
I rode a 125cc scooter for over a year before I got a 125cc geared bike, and rode that for about 6 months before I got an ER6f (the same thing as the Ninja 650r), and my current scooter is an SH300. There are lots of things you learn about on a smaller bike, particularly in the city: observations, road positioning, hazards. Pedestrians, cyclists and cars emerging from gaps in traffic without warning. Truckers stopping to let a pretty girl cross the road while you're going down the inside bus lane, and of course you can neither see over nor through a truck. In the city, you learn to be acutely suspicious of gaps forming and avoid riding close to stopped cars, whether parked or not.
But many of these things are either specific to big city navigation and filtering, or you would learn in a car in any case. In a typical American city, you don't have the kind of filtering you see in London, much less somewhere like Taipei, and you can take for granted that the guy considering getting a bike can drive and probably has for many years.
Furthermore, there's a whole other level of learning that only happens when you're on a big bike. A 125cc geared bike is so incredibly light - it's almost like a bicycle - that you have no worries about dropping it when stopping using poor technique - braking with the front while turning, for example. And it has so little torque you'll never notice a cold rear tire slipping out on an aggressive corner, because outside of gravel on the road or wet manhole covers, it'll never happen. Not to say it can't be fun. I had plenty of launch practice: hi-rev clutch-slipping to clutchless shifting, eking out every scrap of acceleration I could. But it's not long before the stuff you're learning isn't transferable to a big bike.
So I think it depends on how much road experience you have, where you're riding, and what kind of riding you plan on doing (cities favour smaller bikes). A modern 250 or 500 probably would make a better beginner's bike. But 500cc bikes are pretty rare these days, and while 250cc are just on the edge of enough power, I don't think you'd want to have one for more than a few months, unless you're using it as an alternative to a scooter in the city.
As a bonus, they are honestly very solid balanced bikes you could ride your whole riding career. The EX250's have notable shortcomings if you will only own one bike, for many years. I certainly advise starting on a smaller bike and upgrading, but many people obstinately refuse that course. I'm not sure if they are afraid of losing money in the process, or if it's an ego thing.
I did have a ninja zx6r for a few years, and it was a lot of fun. And I did prefer the curvy roads with that bike. Rides were short and intense, like a roller coaster.
But if I'm going on a 500 mile ride, I don't want it to be a roller coaster. Or even a 50 mile ride for that matter.
So yes, you'll want to spend some time in the hills and curves. Don't start on an all-out superbike with torque that kicks in suddenly at high revs; start with something with a flatter torque curve, like a midrange twin (e.g. SV650 or Ninja 650r) or detuned 600. An unfaired bike, if you don't mind the looks, will feel faster from the wind blast. Most of the fun in a bike is from acceleration and corners, and on the street rather than on a track you'll want to have that fun at perhaps surprisingly low speeds. Taking a tight corner at 30mph is harder than it looks, takes more skill than a long curve at 90, and is a lot less dangerous if you crash. I've had a low-sider on my scooter (it was new to me and I didn't know its lean angle limits well enough) at about 25mph in a t-shirt and jeans (but full-face helmet, as always), and walked away with nothing more than a scratch on my arm and a few more scratches on the fairing.
You'll remember the first time a corner surprises you by tightening up half-way through. But the real warning signs come earlier than that IMO: if you find yourself letting off the throttle half-way through a turn rather than smoothly accelerating through it, or changing gear half-way through, that's a sign of poor technique and / or poor reading of the road. Even more dangerously, you can end up learning these mid-course correction habits and think you're doing well, building false confidence.
Bikes are fantastic fun and don't let the raw statistics dissuade you too much. You'll see a lot of idiots on the road doing stupid things, and get a better idea of where the stats come from. Filtering, where legal, can be intoxicatingly enjoyable. And you'll appreciate differences in road geography to a huge degree.
I've ridden in Belgium, Netherlands, northern CA, northwest France, Luxembourg, UK and Germany, in approximately increasing order of fun, though for different reasons. Belgium has terrible (back) roads and is mostly flat; northern CA has some very curvy roads, but they are often very narrow, poorly surfaced and have double-yellow no-overtaking lines to an extreme; though it does have filtering. UK also has many fairly poor country roads - a lot of hedges blocking views - but makes up for it with filtering. Germany is strictly anti-filtering, but has very high standards even for curvy minor roads, which are wide and have high speed limits (depending on state).
(I own a scooter and a big bike and live in London. Scooters are better for filtering in the city, and a lot more practical. I don't own a car, and only ever take public transport if I'll be consuming alcohol.)