While you can choose other fields, we generally recommend using the Alias as a means to track your third party system IDs in the Raiser's Edge because of the functionality that is available for this field in Importacular. You can watch a video tutorial of this functionality here.
In order to use this functionality, you will need to start by mapping your third party system ID as an Alias. (Please note, we do recommend that you create a separate Alias Type specific to your third party system.)
Next review the Alias Area Settings and ensure that they will give you the results that you want (should users be able to have more than one ID for this third party system, etc.?).
With the Alias mapped. you'll want to work with your Constituent Area Settings to enable a lookup field for this information. When you've enabled the field, then you'll need to open your Constituent mapping and add the source field value for the ID number to that row (shown below).
You should also check your Criteria Sets and ensure that you have enabled the option to search for an Alias.