Buying mail order when you don't know your size is always a risk. If you can get to a local bike shop, then that's what you should do.
The critical dimension for fitting is length rather than height. The ratio of length/height varies so you cant always tell. It can vary between different sizes of the same model (ie smaller bikes are proportionately longer). It also varies between brands.
Generally within a brand, most bikes of the same style/size share the same geometry.

Length consists of 3 elements.
-Frame length from seatpost to headtube (in a man's bike, the top tube or where the TT is slanted, the virtual TT)
-Seatpost layback. Seatposts connect to the saddle using a clamp. This may be inline with the post or may be set back a few cm, pushing the rider back over the pedals. You can switch them to adjust the saddle position beyond the adjustment rails.
- Stem length. Most bikes come with a stem which is appropriate for the frame size but you can change it for a longer or shorter one to fit your reach. Some bikes come with an adjustable stem.

The "correct" length is entirely personal, there is no formula. As a new rider, you will probably prefer a short reach but with time, your position will generally get longer.