Paste layers are used to fabric stencils for screen printing solder paste onto the boards.
Both the fabrication of a stencil and using it are distinct tasks you have to pay for. While some PCB manufacturers may also offer stencil manufacture, it is a distinct service. Further, to fabricate a useful stencil you need to specify the material, dimensions and in theory mechanical interface with the stencil printing machine.
So no, you don't need to include a paste layer when ordering PC boards.
And when having boards assembled, you would not include a paste layer for any side of the board that you did not want to print with solder paste - paying to run a blank piece of stainless steel through a stencil production line and then paying someone to flip the board to a second side in the paste printer only to squeegee around solder paste while depositing none of it wouldn't really make sense ;-)
For through hole components you need a different fabrication process anyway, such as wave soldering or selective soldering. Talk to your assembly house (ie, the vendor who populates the boards, which is not necessarily the one who manufacturers the PCBs) about what services they can provide, what materials those require from you, and what limitations such process imposes on your design.