I have a similar setup with dual 23" widescreen Dell IPS monitors. They are hooked up to both of the Thunderbolt ports on my 13" rMBP (via Thunderbolt to DVI connectors). VGA is the older analog signal and probably shouldn't even be included on modern monitors.
You could also connect one monitor via Thunderbolt and the other via HDMI. Either will work fine. Many even prefer to have a Thunderbolt port available to connect external drives and other peripherals to.
The reason I use both Thunderbolt ports for my monitors is because they are both on the left side of the laptop, and therefore by arranging one monitor to my left, the other facing me, and my laptop on my right, I have a natural concave formation and have full access to 3 screens. The cables are very seamless and out of the way.
OSX Mavericks is meant to be used on multiple screens and each monitor will automatically be independent unless otherwise specified. Just go to 'system preferences' then 'displays' and then select the arrangement that best suits you for your setup. All it takes is dragging your cursor from one screen to the next. The integration is incredible.
If you run both monitors with your laptop in clamshell mode, it must be plugged in and charging. Otherwise you can run on battery as long as your laptop is open.