Depending on the type of engine and year of production, your car might need engine oil to meet any of the following MB Spec Sheets:
229.3 (older petrol and non-DPF diesel engines)
229.31 (older diesel engines with DPF).
229.5 (newer petrol engines)
229.51 (newer diesel engines including DPF-equipped cars)
Your owners manual should say what is the right oil spec for your engine.
If you are unsure, then just look for the 'MB Spec Sheet 229.51' label on the oil container, as the new spec is suitable also for older engines.
As for viscosities, 0w-40, 5w-40, and 5w-30 are commom, 5w-30 is probably the best bet for UK climate.
With regards transmission oil, if it is automatic then the original MB-branded ATF is recommended.