It totally depends on the project. If you have purchased a kit, the needle should be included.

Counted cross stitch -- usually a blunt needle called a Tapestry needle (because you will be stitching between threads not thru them). The size will be determined by the floss to be used, i.e. one or more strands of cotton floss vs 1 strand of wool.

Stamped cross stitch -- usually a sharp needle called an Embroidery needle -- with this process you may need to split the actual threads of the fabric. Size again depends on what floss you would use.

Needlepoint -- usually done with a fairly large blunt needle because the design is stitched on a canvass background (thus thru the holes). Again, size depends on floss.

We really need more info on what you're planning to made before we can give you specific information.