Well, you could try my technique. My wife was a bit negative about a bike until I increased my life insurance coverage substantially. Then she began encouraging me to get the bike. "Don't you need at least 1000cc in a sport bike, dear? Why waste money on a helmet?" I always know
exactly where I rate with her.....
As has been suggested, take the MSF class. It's required in some states in order to get the motorcycle endorsement on your license. Even if not required, it's essential.
All the gear, all the time. Full face helmet, jacket, gloves, leg protection, boots. Always.
A 250cc bike will be a bit underpowered at your size. I started on a 500cc Ninja (around 50hp) and it was just about perfect. Rather than cc's, pay attention to HP and weight. In a standard style bike, get something in the 50 to 75 hp range. Something like a Suzuki SV650 (
https://ultimatemotorcycling.com/2019/10/05/2020-suzuki-sv650-abs-buyers-guide-specs-prices/ ) could be a good choice for you to start with. New ones are about 73hp, and the older bikes are about 64hp. Comfortable riding position, enough performance to merge onto a highway without getting squished, no body work to damage when (not if) you drop it.
Let your budget dictate new vs used and how old, but if you buy used be sure you know how the bike was treated. Take an experienced rider with you to look the bike over.
Don't worry about your age. The older I get, the faster my bikes. I figure every passing year I'm putting less and less of my life at risk.
And concerning the wife, remember - there are lots more women in the world than there are motorcycles.