Looking at bikes and narrowed done sizes but a little confused.

I'm a public transit and bike commuter but the bike I commute with is a mountain bike and I'm looking to make the transition to a city/road bike for around $200-250. I'm not a racer. I just need something a lot more lightweight to get around and add messenger bags to the rear.

According to a bike sizing website, I should be looking at frame sizes of 22". I'm a 5'7" small frame female and most of the women's bikes look meh/designed for riding with skirts. I've looked at men's bikes with 22" frames and 700cc wheel sizes - the specs say it should fit people from 5'8" and up. Is that too high for me?

I've looked at GMC Denalis so far and they're in my price range with decent reviews.