The posing table (really a grooming table with the leash holder removed!) is used when the client wishes to be photographed with their dog, usually in some 'confirmation' pose. That's kinda the dog-show convention (which I've messed up locally, I'm happy to say!) but I'd rather do the more isolated shots.
I roll down the paper onto the floor for those shots, and roll it up so that folks aren't standing on it otherwise. Puppies do tend to 'mark' the paper ... I just cut it off as needed.
Look for a local pro store that sells Superior papers ... if they buy them in bulk, you can take a roll home for less than $40. If they buy them in "onesies" you'll pay more, because of the shipping on those heavy tubes! But Superior is my favorite brand. You can make a stand, or buy a portable one; I bought one, and actually cut my paper to a more appropriate width for the shows. (You can buy paper in 53, 106, 120, and 144 inch width ... sometimes the really wide stuff is limited in color selection.)
I use cheap imported wireless strobe triggers, purchased on eBay for under $50 new!
I have also used a pair of Vivitar 285HV flashes, with plastic diffusers, for this kind of work. Strobes are better, but use what you have!
You could use a couple of Alien Bees (with umbrellas), a simple paper stand, a wireless trigger, a roll of seamless, and a simple table with a skirt (under $1K for all!) and you'd be good to go.
Ken