Earthenware and Stoneware Clay - which should I start with?

​This is a good question, but it really depends on what you want to make.
 
There are loads of clays out there to choose from, but in the kil.n.it onsite Materials Shop, in our office, we have found it is easy to start with a white clay (to allow you to have any colour you want down the track) and then simply choose if you want a functional object (stoneware recommended) or a sculptural, experimental piece (earthenware recommended). 
 
Of course these are only ultra-basic recommendations and you can make functional objects form Earthenware clay, and Sculptures from Stoneware.  
 
What is really important about the distinction between the types of clay is the firing temperatures.
It is important to be aware of the firing temperature of the clay you are using as it means this is the temperature the clay is designed to be strongest, most dense and durable. Beyond or below these ranges can lead to brittle or weak objects.  Most importantly, you need to stick to that temp range when it comes to choosing glazes and glaze firings.
 
Earthenware is usually (for most glazes) about 1080-1100 degrees
Stoneware usually is 1280-1300 degrees, 
However each manufacturer or recipe can be different, so don't assume, double check!
 
If you accidentally forget, not even a technician can guess with you. It is best to assume you are using Earthenware, as over-firing your clay to temperatures higher than recommended means the clay itself begins to melt!