Your subject
I’ll be working off reference photos that you provide but the portrait is not restricted to what’s in the photo. For example, photos of multiple pets can be composed into one such as the one below. Is there a favourite toy to be added? Is there a particular setting you want for the background? What are the special qualities or physical characteristics you want to come across? Knowing what “feel” you’re going for will inform the other considerations.
Size
If you already know where you want to display your portrait that will guide your decision on size. Bear in mind how you would like to frame it. A 9×12 painting, for example, could be matted and framed to be much larger, such as 12 x 16. Alternatively, if you go for a portrait on stretched canvass, no framing would be required so the canvass size itself would be the final size.
Three separate pets using different reference photos composed together.
8×10 drawing in 11 x 14 frame (matted).
Subject placed in a grassy scene not from the reference photo.
Media
Your choice of media will depend on what your overall purpose and looks of the portrait is. Some thoughts:
Acrylic paints are suitable for all kinds of portraits. They are typically painted on a gallery-wrapped canvas that requires no framing. The side edges are painted black (or whatever color you want) so the portrait will be ready hang. Alternatively acrylics can be painted on canvas paper that provides endless options on framing.
Watercolors are painted on cold-pressed paper and will need to be framed. Using watercolors, the portrait can have a softer feel.
Drawings are a wonderful alternative, especially when choosing a smaller size portrait. They look great when the frame and matting are much larger than the drawing itself.