Peonies are one of the ones that do not like being moved at all. The best idea is to put your peonies in a spot where you intend to leave them for many years. If you do intend to move them, be aware that they may choose not to flower for several years. Irises are best moved and divided in late summer, but if you move them in spring, do it as early as possible, before they've grown too big.
Irises tend to be aggressive growers and heavy feeders.
Usually, they need to be divided every three years or so. If moving them in the spring, avoid small divisions so that the plant is not too greatly disturbed. Otherwise, they might not produce blooms. You can dig up the tubers of Jersulelum artichoke and move them either before they sprout, or when they are no more than six inches in height. Lanceleafed rudbeckia can be moved when it first leafs out, however, unless you get the whole root out, it droops.