I take my current hourly pay rate for my day job, and multiply by 1.5. If they don't want to pay that, it's my weekend and not worth my time. With that being said, $20/hr is undervaluing yourself.
as far as them providing the pig, its up to you. If it was me, i'd tell them where to get it, what size it should be, and any special requirements, does it need to be butterflied for your pit, are you going to do it race car style?
L trailer spicewine, webers, 2-26.75's, performer, heineken 22 1/2, 7 level pro-q 20 excel