Clustering Customer Data
The answer could be anything according to your data! As you can not post your data here, I propose to spend some time on EDA to visualize your data from various POVs and see how it looks like. My suggestions:


Use only price and quantity for a 2-d scatter plot of your customers. In this task you may need feature scaling if the scale of prices and quantities are much different.
In the plot above, you may use different markers and/or colors to mark category or customer (as one customer can have several entries)
Convert "date" feature to 3 features, namely, year, month and day. (Using Python modules you may also get the weekday which might be meaningful). Then apply dimensionality reduction methods and visualize your data to get some insight about it.
Convert date to an ordinal feature (earliest date becomes 0 or 1 and it increases by 1 for each day) and plot total sale for each customer as a time-series and see it. You may do the same for categories. These can also be plotted as cumulative time-series. This can also be done according to year and month.


All above are just supposed to give you insight about the data (sometimes this insight can give you a proper hint for the number of clusters). This insight sometimes determines the analysis approach as well. 

If your time-series become very sparse then time-series analysis might not be the best option (you can make it more dense by increasing time-stamp e.g. weekly, monthly, yearly, etc.)

The idea in your comment is pretty nice. You can use this cumulative features and apply dimensionality reduction methods to (again) see the nature of your data. Do not limit to linear ones. Try nonlinear ones as well.

You may create a graph out of your data and try graph analysis as well. Each customer is a node, so is each product when each edge shows a purchase (directed from customer to product) and the weight of that edge is the price and/or quantity. Then you end up with a bipartite graph. Try some analysis on this graph and see if it helps.

Hope it helps and good luck!