It's true that probiotics can help with acne. There's a real connection between gut health and skin health
(see the linked post for detailed explanation). For example, bacterial overgrowth in the gut is more prevalent in skin patients than in healthy controls. Also treatment with probiotics or fermented dairy beverages have been shown to help with acne. So gut health is definitely a factor in skin health. Maybe not for every acne patient, but it's worth investigating anyway.
That said, I'm not sure that probiotic supplements are the best option. Because of lack of regulation you really don't know what's in the supplements. Independent tests often show much lower numbers of colony forming units than what's shown on the label.
Why not just make your own fermented foods? Making yogurt or kefir at home is dead simple. As is making sauer kraut and other fermented vegetables. Check the book Nourishing Traditions from Amazon for plenty of recipes.
When you make your own fermented foods you are sure that you actually get those probiotics. Also, studies tend to show that probiotics only have transient effects on the gut bacteria. When you stop taking them the bacteria just reverts back. That's why I think it's better to 1) get your probiotics from food so you don't have to rely on supplements 2) eat prebiotic foods that feed probiotic bacteria.