I always tell people who are getting ready to buy their first bike that they should absolutely 100% buy the first one used. Better yet if it is already scraped up a bit, and this is because a lot of people drop their first bike (I did not. I ended up dropping my second one, which was nicer and newer, on a damn grassy hill I had gotten used to using while leaving work . . . dammit). You will not be guaranteed to drop it, but it's not an uncommon thing for a new rider.
As for starting size, this is always a topic of debate. First, it depends on the kind of riding you'd like to do. I've always wanted to ride sport, and that is how I started after the MSF. I got a somewhat beat up 04 CBR600RR. That was a big jump, no lies (250 twin to 600 i4). However, I grew a lot on that machine, as I also did on my 07 GSX-R750 (RIP). It honestly is different for everyone, what size is good. Keep in mind it's not just size (cc), but engine type and bike weight. Four cylinder sport bikes, although they come in 600cc at the small end, still produce a lot of power, more than a 750cc twin would. In general, 600cc sport bikes have a relaxed power band until close to 10,000RPM. This means they can be putt around somewhat (they can also be very fast and surprising to a new rider). The biggest hurdle is not starting/stopping or riding in a straight line for a new rider. It will be proper braking, turning, and exiting turns. That whole process and development of that set of skills is crucial, and learning on a supersport will likely make the process harder than on something smaller.
If you wish to do long distance riding, it is possible on a sport bike. However, there are only "relatively comfortable" rides in the race replica class. While I am perfectly comfortable and can do it for hours, it's not as comfy as sitting upright like on a standard. In general if you are doing lots and lots of distance riding, I'd shy away from a sport bike, especially if you aren't really planning on riding fast on twisty roads (and a lot of sport standards can do an excellent job at this, anyway).
In the 250cc class, I personally favor the Ninja 250R. They are harder to find used, but they are around if you look. They hold their value very, very well.
Whatever you buy, make sure you get adequate gear. Starting at the top, this means getting a full face helmet. I would recommend getting one that is DOT/ECE certified, or if you are willing, DOT/SNELL2010 certified (there are a few models out now that meet the 2010 spec that are nice). Don't try to save money by buying a cheaper helmet that is practically off brand and only has a DOT sticker on it. The employees at the shop should be able to help you find the correct helmet fit, but in general it should be tight on your head, but not uncomfortable. To test this, keep it on your head for a few minutes and make sure you do not feel pressure points. Helmet shells come in different shapes, and not all brands/models will fit your head. Try on a bunch of different helmets to see what you like.
As for a jacket, get one that has CE armor in it (including a spine guard). If you decide on a textile (which I personally do not like), do NOT get a mesh jacket. That mesh will easily disintegrate in a crash, making the jacket essentially worthless. I've seen the after effects and they are not pretty (road rash is not cool). I personally favor leather, as it is worn as almost a second skin. Its heavier nature makes it so that it does not flap around in the wind. Textile jackets, on the other hand, will do this. The downsides of leather are that it requires more care and is more expensive. Generally leather will outperform textiles for crash abrasion resistance. Good brands for leather (that I have seen) include Icon, Alpinestars, Joe Rocket, Teknic, Dainese, Spidi (my choice). There are a few others out there, but generally you just want something that is constructed out of fewer pieces of leather. This means less leather is stitched together, making for a safer crash garment that will hold up better. This also means it will be pricier, as it's easier to throw a jacket together from many pieces in the slaughter process vs cutting large single pieces for use in the jacket.
Wear tough, over-the-ankle boots. In the event of a crash, you'll be glad you did. As for gloves, get ones that have a decent amount of armor in them to better protect your hands.