Based on myself (6’2″) trying out the bikes you suggested I don’t think any of them will be comfortable for you.
A Ninja250r would work but your legs would be pretty folded up. Older (pre-08) models fit a little better than the newer sharper looking ones.
Supermotos and dual sports are likely to fit better for a light starter bike. They have more open riding positions with bigger seat to peg distances. You should be able to find some decent used ones in your price range though it will be a little harder than finding the Ninja 250 or GZ250 at that price.
In dual sport bikes even bikes like the DR650 or KLR650 may be a good bike to look at. Though the are 650cc bikes they are single cylinder bikes and nearly as light as the 250s and don’t have much more power. Other options are DRZ400(S or SM), KLX250(s or sf), XT(225 or 250) and several others.
Craig