Welcome!
I'm 5'2" as well and had the same budget restrictions as you do. I ended up choosing a Specialized Dolce for my bike. I chose the 48cm, and found out the other day that I liked it so much because it's a perfect fit for me. The price tag is $850, but my LBS was carrying them for $800.
I did a lot of research before making my purchase, and my overall takeaway was that bikes in the same price range from reputable companies are all of the same quality, you just need to ride them to see which one fits better for you.
Good luck in the hunt!