Help With The Preffered Package Type Assessment

Hello there to everyone! I have the question concerning the underlying data analysis methodology. Here is the small introduction.

There is a data from the e-commerce site about its customers' purchases and there are 875 observations total. Each observation consists of 5 values. Scales of value measurement available for each observation (for each customer) are summarised in the following:

1. Package Type (Nominal): Type 1, Type 2, Type 3
2. Sex (Nominal): Male, Female
3. Age Group (Ordinal): NULL, Before 20, 20-25, After 25
4. Location (Nominal Scale): NULL, Region 1, Region 2
5. Orders Count (Ratio Scale): Integers
NULL represents missing data.

The task is to identify which Package Type is preffered by which client type, composed of Sex, Age Group, Location and Orders Count. Put it another way: what is the Package Type must be given the set of charasteristics, consisting of Sex, Age Group, Location and Orders Count?

What am I asking is not a ready solution for this problem - this just won't be so interesting.:) I want you to head me towards the methodology, answering this question.:confused:
What branch of Statistic might handle this problem? Maybe you could advise me some good classic book covering the subject? Any help will be appreciated.

Thank you in advance.
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Thank you for a reply! I heard some techniques of machine learning might be of use here, am I right? What is the defference between MLR and machine learning techniques?