Welcome! Both minis and standards can be great in all of the mentioned sports, so I would suggest first choosing the dog that you most want to live with. Meet some well bred minis and maybe some standards to refresh your memory and you'll probably have a feeling for which one you're most excited about.
There are some general differences between them, but these differences pale in comparison to the variation from dog to dog. Minis have a reputation for being more excitable and driven, while standards are more calm and less drivey. But from what I've seen, it is more that in standards, there is more variation between lines (spoo people may correct me). If you want a performance dog, you'll want to look for a breeder who has titled their dogs in performance sports to demonstrate their drive and trainability. I do not think it is hard to find this kind of breeder with standards. For minis, I think you can find performance pups within a lot of litters, whether they be from show breeders or performance breeders. My mini is from a show breeder, but was chosen as the best performance prospect in his litter. His breeder was great with giving the puppies tunnels and unstable surfaces to play in, and she chose my pup based on his drive and attentiveness. So far I am happy with his trainability and drive. But I wanted him primarily as a pet and I see the sports as ways to engage him. So I'm not concerned if he isn't a top competitor... but we will see!
Regardless of which you choose, you will want a breeder who will help you to pick an appropriate pup.
In terms of competitive success for agility, that will depend on the height of the dog as well as its skills. Border collies and shelties tend to be tough competition in their respective height categories, so I think poodles have had more success in the smaller and larger height categories. That isn't to say they can't be good competitors to the herding dogs, but there is certainly a lot harder competition for those heights, so I think some people purposefully avoid them.
