The bottom is neither succulent or cactus, a type of euphorbia (I think echinopsis). It's a tree, should grow leaves in the summer and is HIGHLY toxic/poisonous. If you ever do much with it and touch the milky white sap, make sure you clean thoroughly, it can kill you. It prefers heat and lots of water during the summer, easily acclimated to full sun exposure, and responds well to a little nitrogen every once in a while.
The next above that one is a cute little stretched out jade plant. I usually top mine before that to let them bush out into mini trees, but they do great with water once or twice a year, not frost hardy and do well indoors during the winter and great in partial sun during the summer outdoors. They are sensitive to changes, so to put outside you'll have to acclimate slowly over the course of a month or it'll burn up.
The top picture from left to right is a type of mammilaria, not certain which. pretty flowers in the summer time, usually white, pink or purple. No nitrogen ever, or you'll get black blisters which can cause rot and kill the plant eventually. Once or twice this summer you might like to give it a small dose of phosphorous only, about 6 weeks apart. Same thing, if you go outside, acclimate slowly, hour a day at first until reaching full sunlight.
The center is an ornamental variety of aloe, still usable for burns, but not as effective as the most common found in stores. It's mostly for looks. Keep that one in shade and partial sunlight, best kept indoors and watered once or twice a week. Fertilizer is almost never necessary, but a weak mix of all purpose once a year helps keep them fresh and vivid.
Unfortunately, I can't remember the one on the right up there, I've had a few before, but treat it the same as the oreocereus and It'll do great. You can either leave the pups on it, or cut off cleanly and dry for a week or two until the cut calluses and pot on sand in the shade to make several new plants. No water til they root, and rooting takes about six weeks.
Hope this helps, enjoy!