I believe that there are a few tools that are absolutely essential for anyone who wants to work in the backyard.
FIrst and foremost, for people who plan on working for extended periods of time, head down to the local Home Depot and get a quality pair of gloves. These will become your best friends, trust me! If you work for a long period of time, you may not notice it until it is too late, but your hands will quickly become chaffed by all of the wood and dirt that your hands will undoubtedly come into contact with.
Next up is the shovel; it doesn't matter what size. You will just want to have one in your arsenal. Many people confuse shovels and spades, but there is definitely a clear distinction between each. Learn it and you won't sound foolish, hah!
Finally, I would recommend something to transport materials with. My tool of choice is the wheelbarrow. A small one is more than enough if you are not doing anything crazy. These can come pretty cheap, but make sure that you get a high quality one. Also, try to get a wheelbarrow with aluminum or plastic handles. Wooden handles will crack over time and these can become a serious hazard for you.
Good luck with your future gardening efforts!