Hi there,
What you'll get to see is quite predictable. Check out the timetables on the Translink website. Here's a quick summary:
A regular DMU service with CAF 3000 and 4000 units
Less regular Enterprise services
No freight
Really rare infrastructure workings
Once every other month(ish) RPSI steam service railtours
(The variety is significantly less than many places in England)
Locations:
Almost every service in NI passes through Botanic station. To one end there are sweeping reverse curves and there's a short tunnel at the other end of the platform. All the NI services stop there and the Enterprise services pass through non-stop.
For a rural setting, by Moira station. Again, the NI services stop there and the Enterprise services pass through non-stop. However there are fewer services than at Botanic.
For more general interest try the beach at Holywood. You have the Bangor trains (2tph each way) on the curved embankment next to Belfast Lough. You have the ferries and other shipping on the Lough and if you look up you have the planes for Belfast City Airport.
Enjoy your trip.
Mr Toad