As I recall you could have either, Valmave. I think the "train set" that I had was provided with a controller that fitted on to a pair of huge "lantern" type batteries. But these soon went flat so I persuaded Dad to get me a 6/12v transformer which was much more satisfactory.
As I said, I had huge problems with the transmission on the tiny loco. It had six powered axles, three each end which were driven by the bands. Looking back I think the main problem was that the spindles coming out of the motor were extremely small diameter (probably about 1mm) and the drive bands simply could not provide enough grip. I tried covering the spindles with various substances to increase the grip, but to no avail.
Although it was over 50 years ago I can remember the set very clearly. It had the usual oval of track and, apart from the loco, there were three maroon BR-type coaches.
Because of the problems I ditched the treble-0 stuff after a short while but kept the transformer when I moved up to 00 (I still have a decent sized 00 layout today).