^^SAP basically has many modules and these modules are often subdivided by submodules. A particular SAP consultant can focus on one or more modules depending on their experience and capacity to learn.
Following is the list of module available in SAP system.
SAP FI Module- FI stands for Financial Accounting
SAP CO Module- CO stands for Controlling
SAP PS Module – and PS is Project Systems
SAP HR Module – HR stands for Human Resources
SAP PM Module – where Plant Maintenance is the PM
SAP MM Module – MM is Materials Management -
SAP QM Module - QM stands for Quality Management
SAP PP Module – PP is Production Planning
SAP SD Module – SD is Sales and Distribution
SAP BW Module – where BW stands for Business (Data) Warehouse
SAP EC Module – where EC stands for Enterprise Controlling
SAP TR Module – where TR stands for Treasury
SAP IM Module – where IM stands for Investment Management
SAP – IS where IS stands for Industries specific solution
SAP – Basis
SAP – ABAP
SAP – Cross Application Components
SAP – CRM where CRM stands for Customer Relationship Management
SAP – SCM where SCM stands for Supply Chain Management
SAP – PLM where PLM stands for Product LifeCycle Management
SAP – SRM where SRM stands for Supplier Relationship Management
SAP – CS where CS stands for Customer Service
SAP – SEM where SEM stands for STRATEGIC ENTERPRISE MANAGEMENT
SAP – RE where RE stands for Real Estate
Basically, one can focus on SAP FI (Financial accounting) with its submodules such as Accounts receivables, Accounts payables, General Ledger, Asset accounting, Bank accounting etc. But the same can also take another SAP module, for instance SAP PSM or funds management (budgeting and planning purposes) or SAP CO (Controlling - management reporting) which likewise has many submodules. Or SAP MM might eventually take on SAP SD (Sales and Distribution)
Which means, these are main modules that comprises SAP. Some modules are not activated basically because it is not required. For instance, if a company is a financial institution then there is no need to activate SAP PM (Plant maintenance) or SAP PP (Production Planning). For some professionals with specific experiences, they can proceed and take on SAP industry specific modules such as SAP Retail or SAP RE (Real Estate) or SAP IS-Oil. However, in my point of view, it is still best to have a knowledge or expertise on the core modules then having the SAP industry solutions' module proficiency due to the event that projects with these specializations are somewhat limited unlike those with core modules which are almost present in some industry such as SAP MM and SAP FI (It is impossible for a certain company not to have Inventories and Accounting as one of their processes, while not all companies have Oil or Supermarket as part of their business portfolio).
Nowadays, companies would get trainees depending on their specialities. For instance, those with accounting backgrounds will be assigned to devote to SAP FICO for training . Those with warehousing and logistic experiences would often be in SAP MM / SD. And if one has programming experience, he/she would be suggested to learn ABAP while those who used to work for Real estate will be in SAP RE.
Simply because the technicalities are easy to learn while the business process familiarity takes time to master.
These must be the gauge on which SAP modules are best fit for you.
For learning, there are lots of companies who are willing to accept trainees such as HP, SMITS, Accenture, IBM, Fujitsu Enterprise Solutions. However, do note that they will offer you the lowest possible rate (not sure with HP as I know they quite give a very acceptable offer) as they will be banking on you to learn while they put you on the job. It is more like a On the job training kind of setup at first but once you reach the second year, you will already feel the hang of it.
I also have my share of colleagues who "dropped" out because they feel long hours of work does not suit them well. But in my personal opinion, while the pay for trainees are hideously low, the payout eventually will be even more abundant as you gain more experience or, in the point of view of your employer, become their cash cow.

I have colleagues who accepted salaries way lower than what they previously had but the three year training actually paid off and they are now one of the high earners I know. I also had a accountant friend who declined the offer to become a SAP trainee because of the 3-year bond. Now, she's still an accountant but her supposedly batchmates have now earned more than average.