I am planning to buy a set of rear rotors (OEM) for BMW 323i Sport Pkg (Yr 2000).
I know the brand of rotors is Brembo and the part number is 34211165563, but I need to confirm the size.
One website says "Vented 294x19mm" - can anyone tell me if
that is the correct size? There are others out ther with size 276x19mm so I am confused.

Brembo part number 34211165563 is a 294 X 19 mm rotor and was the standard BMW 323i rotor. A new one costs $38.

Brembo part number 34211165211 is a 276 X 19 mm, cross drilled, vented rotor (it has small holes drilled through it).

Either rotor would work fine with the brake calipers on your BMW, but don't have a cross drilled rotor on one side and a solid rotor on the other.