Replying to Telephoto lens help

I'm looking for a telephoto lens and cant decided what to get.I have a canon t3i (600d) and a cheap tripod. Looking for a lens in the 70-300mm range. My price range is low, only looking to spend around $500. I want to use it for filming surfing and skiing. I seen the tamron 70-300mm f4-5.6 VC looks like a good cheap lens, not sure how it handles filming (test shots I've seen look poor). Or should I spend the extra money and get the canon 70-200mm f4? Also is it hard to get a stable shot with the canon 70-200 f4 without IS? Open for other advice.