I manage a Best Buy and personally love the robot vacuum technology. We've had a robot vac for about 4 years now and love how clean the house stays with very little effort. No more dog hair stuck to the bottom of my feet!
First tip: Don't start cheap to "see if you like it." One of two things will happen. Either 1) you won't like the cheap one and will have wasted your money, or 2) you will like it but wish you bought a better one and will upgrade (in my case twice!) and will have wasted your money. Just start with a good one and enjoy it! Stay away from any no-name brands. iRobot and Neato are the only two worth looking at. Both companies make a great product and have great customer support. Shark is a recent entry into the game. While Shark generally makes great vacuums, they haven't been in the robot game long enough for me to give a solid assessment. I will say this: Shark is a vacuum company that made a robot. iRobot is a robot company that makes vacuums. iRobot has made Mars landers, bomb disposal robots, mine sweepers, and search & rescue robots.
Navigation: Get an iRobot i7 or s9, or a Neato D7 (we'll talk about the iRobot + models in a sec). These models use intelligent navigation to know where they are in the house. This gives them the ability to be sent to clean specific areas, like cleaning just the kitchen or the living room. They can also recharge in the middle of a job and resume where they left off if the job is too big to complete on a single charge. You can also create virtual barriers to keep the robot out of rooms or away from the Christmas tree. These models also clean in a deliberate back and forth pattern, while the cheaper one randomly "pinball" all over the place.
Power: The D shape of the iRobot s9 and Neato D7 put the brush right up front and allow room for more powerful motors. These two models do the best job of cleaning both carpets and hard surfaces.
iRobot + models: The s9+ and i7+ have a base that will empty the robot for you. The base can hold about 60 days' worth of dirt before you have to remove the bag and throw it away. This is a really cool feature if you aren't at home much or are just too lazy to empty the robot daily. However, the + feature does cost $200 more than the same model without it, so you have to decide if it's worth it for you. Personally, I've never found emptying the robot to be that big if a deal.
(Incidentally, I named my vacuum Rosie, lol!)