How to choose the right size bike? This question is one that I'm sure has been beat to death, but I am new to bike riding. Ideally I would have bought the bike at a local bike shop and been fit for the perfect bike. However, the prices at the local shops where I live are pretty steep. So this is my predicament.
I am approx. 5'6&quot; to 5'7&quot; (Please resist the urge. I know I'm a manlet.)
My inseam is roughly 29.5&quot;.
The frame size of the bike I ordered is 50cm and the sizing chart is below.

Did I get the right size?
Since you are new to cycling... I would say you made about as good of choice as you could have given the information.  I know two people 5'7" and one likes 52cm frames and the other 48-50CM frames.  The point is, the difference is subject to preference based on body type (e.g. short legs-long torso vs long legs-short torso).

Once you get the bike there will be a number of adjustments (seat height, seat position, handlebar height) etc that can be made to dial things in just right.  

Finally, really try to understand the frame geometry of this bike so if and when you get your next bike you are vary familiar with the specs what you like what you wished was different etc... so you make the best possible choice in the future.