Mine webshop history for clusters I've no experience in data science so this will be one of those questions...

I have data from >100k purchases made via a webshop regarding a catalogue of around >100 items. The history of purchases flattened out looks like

Item1 Item2 ... ItemN Sex State
    5     0         0   M    NY
   25    15         0   F    IL
    0     1         1   ?    NY


By playing around with the data, I can deduce simple facts like "90% of all purchases include at least 3 Item1", "If there are at least 4 of Item2, it is likely that Item3 is 0" or "60% of all customers from NY are male, but only 40% of those from IL are". Given the amount of combinations and data there is, the most obvious question: How can I approach wringing out more information from a data set like the above? I'm mostly interested in how one item does or does not entails inclusion of another...
Frequent Item-Set Mining is what you are looking for. You can see the tree structure of your frequent itemsets and the association rules afterwards.

For your data I'd suggest to look at the whole for a while to get a sense on what you have in hand. Playing with concepts like Probability Distributions, Entropy, etc would be really helpful in case you can reduce the size of your features. 

PCA also gives you the opportunity of projecting your data into a low-dimenstional space and you can see also plots showing first several PCs in 2-D or 3-D and get an impression about your data.

Before all above I strongly suggest to see if you have Missing Values and if yes try to cope with them.