Hardwood floors look better laid so that the planks go in the longer dimension, in general. Laying them the shorter dimension will make the room look chopped up. Think of how a hallway would look with the planks going across it rather than lengthwise. same thing, but less obvious. You need the planks to flow into the hall or next room.

Planks look better laid the long way. Why take up the lino, let it be a vapor barrier if its not all torn up. I have covered over my lino floors in the kitchen with quality laminate.