Generally speaking, that's easy to answer--the one you like best and can afford. Obviously, there can be a lot more to it than that.
Here are the primary considerations: price range, quality of photos, size of camera, bells & whistles.
Let's start with price range--You can start from around $50 (I don't recommend it) and go up to--well, the sky's nearly the only limit on that but $300-$500 is generally the top level most people are willing to expend for a "point and shoot" camera--a camera to be used for social occasions rather than professional work.
The quality of the photos will be impacted by the number of megapixels, whether or not the camera has image stabilization, and a few other factors that really are based on the price.
Size is simple--they're small! I believe the largest one on my list of nice cameras is 4.1" long. That will fit in most pockets with ease. Don't let the size fool you--these are powerful little guys.
Bells & whistles can be fun but not necessarily critical. I love that mine can be switched from automatic focus to manual so I can make adjustments if I want but I don't think I've ever taken advantage of that feature. It's lovely to have an LCD screen that will flip around so you can have the camera near the ground without having to be down there at the same level in order to see what you're aimed at--again, not necessary. Think about these things, though, as you think about which camera you might want to buy.
Do your research, look at the higher end models and see which features you like, which you really like, and which ones you really don't think you want to live without and then start checking out cameras to see what fits your list of things you want and your budget.
What's most important? Is it comfortable? I'm serious! When I was choosing between two cameras that were so close in price, quality, and features that I couldn't make up my mind, I put each of them in my hand (it really is important to be able to hold a camera before you buy it, even if you go back home and order it online) and bought the one that felt best. Not only did I like the way it felt when I held it, the shutter release was at the perfect location. My right index finger went there automatically. On the other one, my finger headed for the on/off switch. That made my decision for me.
Bottom line--you're the only one who can decide which camera is right for you but buying after doing a little research with help you get not only the one you want but also the one that will give you the most of what want to get out of a camera.