A few questions,Are there any concerns to normalizing data to be within the range 0 - 1 and mean centering the data as well? Does it matter which comes first?If you do one, is the other not required? 
What does normalizing and mean centering data do?
preprocessing
Welcome to DataScience.SE! If you don't center before you normalize, you either don't take advantage of the full [0,1] range if your input is non-negative. The combination of centering and normalization is called standardization.Sometimes one normalizes by the standard variation, and other times by just the range (max-min). The latter is called feature scaling. The effect is much the same. Normalizing by the range is easier computationally. Normalizing by the standard deviation fixes the sample variance, which is nice from a statistical perspective. When using the standard deviation, the subtraction is usually against the sample mean rather than the minimum.There are several reasons for performing standardization. Sometimes we are interested in relative rather than absolute values. Standardization achieves invariance to these irrelevant differences. By explicitly preprocessing the data to reflect this disinterest, we relieve the model from having to learn it, allowing us to use a simpler one. Another reason is computational; it reduces the condition number -- you can think of this as the skewness or niceness of the loss surface -- making optimization easier and faster.