The sod cutter carves sod into strips and slices under the sod to separate it from the soil so you can roll it up and reuse it elsewhere in the landscape. When you have to excavate a large area, loosen the soil with a garden tiller first to make digging easier. If you have to dig a number of postholes for footings or to build an overhead structure or fence for your patio, rent a power auger. The two-person version in the photo will bore through soil and small roots easily. You can use a hand auger or posthole digger if you have just a few holes to dig.
You'll need a tamper whenever you excavate or fill an area. Sand and gravel base material for concrete and stone surfaces should be tamped too. A hand tamper works well for small areas, but consider renting a power tamper for large patios and long paths or walks. In footings and holes, you can tamp with the end of a 2x4.
Image, from left to right: Hand tamper; Garden tiller; Mattock; Shovel; Power Auger; Garden rake; Crowbar; Power Tamper; Lawn Edger