A camera is a tool, not a magic box. If you do not know how to use the tool, you will still get bad photos. In other words, you are asking too much from a camera. You need to learn how to use a DSLR if you are trying to shoot sports (which is what I am guessing you are wanting to do). Lazy and automatic won't cut the mustard.
That said, the fastest camera with the biggest buffer for the budget you have indicated is probably the Pentax K-r. It can shoot at close to six frames per second for up to 30 frames. Buffer clearing time would be approximately 12 seconds after those 30 shots. The only way to get faster is to spent significantly more money.
You can buy the K-r in a two lens kit that come with 18-55mm and 55-300mm lenses for under $800. However, brighter telephoto lenses are not common for Pentax cameras, so the kit is only good for daylight sports photos. Canon and Nikon cameras have many more lenses to choose from, but a bright telephoto lens would cost more than your entire budget.
I need a recommendation for a dslr at no more than $700. My current camera buffers every so often, holding things up as much as 45 seconds or so. The focus is not as quick as I would like. And, I want sharp, sharp, sharp. I understand these variables might be difficult to match on one camera, from what I have seen, especially at the cost, but I'm hoping someone has some good ideas. I'm lazy so go with automatic typically, therefore not overly concerned with a lot of adjustments. I will be purchasing a separate telephoto lense, so any any recommendations on a brand (can I go with other manuf's than who builds the camera?) Thanks so much...Amy