If you are getting your betta from a petstore, look at the betta carefully. Is it active (as active as it can be in such a teeny container)? Is it colorful? Are the fins either flaring or flowing gracefully? If the betta doesn't show good color, seems sulky or uninterested in what's going on, or has fins clamped close to them, you should pick a healthier looking fish. One that's colorful, with grace in the fins, and who is responsive to surroundings.
If you are ordering a betta (or multiple bettas) off the internet, looking for signs of health is something you have less luxury to do. You basically have to look at pictures of bettas with descriptions and decide from there, although most reputable breeders would not ship a betta if he/she is unhealthy, so you usually won't have to worry about that.
When you first get your betta home, it is a good idea to float the bag in your own water for about half an hour. Do not just put the betta right in his new home. It may be tempting to want to see him in all his glory right away, but what you may end up seeing instead is a fish that dies from temperature shock, PH shock, etc. So it is best to just float the bag in their new home for about 1/2 hour so that doesn't happen.
First off, let me give you the dreaded betta-in-a-vase lecture. When you see a betta in a small vase with a plant, they will often come with directions saying never feed or clean the vase. Well, how would you like me to tell you that you must now live in a closet the rest of your life, wallowing in waste and eating nothing but the clothes that are hanging in there. Chances are you really wouldn't like that too much, and chances are you probably wouldn't live long, since you should be eating food, not clothes. Likewise, the betta living in a vase would be like you living in a closet. The not cleaning out forces the fish to wallow in waste, and since they're carnivores (they eat meat instead of plants), they would starve to death on just plant roots. If you want a fish with a plant, then get a large vase (at LEAST one quart, preferably more) and put your own plant in. And above all, FEED AND CLEAN YOUR BETTA REGULARLY!!!!
Now that I have the vase lecture off my chest, let's talk about other containers. A tank that is a couple gallons would be like the Hilton Inn for bettas. However gallon, half gallon, or quart mason jars would suffice. The quart jars should be cleaned minimally twice a week, but clean more if the water gets cloudy. This should be a 100% water change. I personally like the mason jars, although if you have females, they can be in a tank with each other. Do NOT get the pint mason jars. Again, like the vase, it would be like living in a closet.