+1 on the gear.
Be prepared to spend money, don't skimp, and buy the gear that feels as comfortable as a second skin so you will have no excuse not to wear it all the time. An expression used here a lot is ATGATT. (All The Gear All The Time).
Fairings can be replaced. Skin can't.
I have the same build as you, so I would suggest you're looking at about $1000 to get yourself from zero to ready-to-ride.
Figure $250 each for a good helmet and a good jacket. $150 each for pants and gloves that will protect you in a fall. (if you just can't manage both in the budget, spend what you can on gloves).
Footwear. Some will say that you can get away with workboots. I did it my first year back on the horse; but since my first ride at the end of last season wearing a proper set of riding boots, I'll never go back.
You're correct in thinking that a 250 would be a bit small to the point where you will likely feel uncomfortable and off balance. You'll get that sensation during your riding course.....that you are planning to take before you ride your own.....
JKV has it right, I would not recommend going any bigger than 600cc for your first (USED) bike. It will already be a lot of power on tap for a new rider. As your ability and experience matures, then you can look at something larger.