Buying a bike to ride with a baby seat

[FeedmeSeymore]

My favorite bike was a late 80's Steel Raleigh road bike. I loved it and it felt great, as a daily commuter and in the mountains on weekends. That bike got stolen and I replaced it with a no name aluminum bike, and it ruined riding for me. Everything just felt wobbly all the time.

Now I am living near Nashville and looking to get back into riding with my 20lb toddler in a front mounted seat. I will probably only be going on paved trails for a maximum of about 18 miles round trip. There is one big hill between my house and the trail, so I might need some granny gears to get up with the weight of my toddler plus my extra pregnancy lbs. I figure I will need a bike with a more upright position to fit the seat between my body and the handle bars. I also think a women's step through might be safer to mount and dismount with the baby seat, maybe this is a non issue though.

I'm looking at this from REI, but I'd rather buy used and spend under $500
https://www.rei.com/product/109676/co-op-cycles-cty-21-step-through-bike



Could I just get a used 80's-90's steel road bike like what I had before and lower the seat and put on some mustache handlebars to make it more upright? Should I get a size down from what would normally fit me if I want to do this? My inseam is 32''

How can I tell the difference between a quality "vintage" bike on Craigslist and a junky piece of rust. Most Craigslist folks don't even know the size of the bike they're selling let alone the year. What questions can I ask to narrow down my search without driving all around looking at every bike in person?