Hi Maria,
The White sewing machine in kpmom link is a Vibrating shuttle model so White Rotary needles or 15x1 are too short unless lowered. White Rotary needles and bobbins are fine for a White Rotary. The VS model uses the longer 20x1 needles and a long bobbin with the hollow shaft which are somewhat difficult to find and expensive (bobbins). Nothing terrible though. Lots of rain here, finally getting decent weather.
The OO, O, 1, 2, 3 needles sizes are meant to confuse to create needle loyalty and are obsolete. Best looked at as a 00 being fine and 3 being coarse. Best to use Singer and European sizing which is easiest explained by googling. I'd probably create more confusion by attempting.