You can grow chili peppers in pots using any standard potting soil. They are actually very tolerant of a wide range of soil pH and quality. For someone growing a few pots of peppers and perhaps not much else, an excellent and economical option is a potting mix that has slow release fertilizer mixed into it. One brand that is very popular and available at most garden centers is Miracle Gro, which has several different formulations including a mix for vegetables that would work perfectly for your peppers.
There are also "organic" soils available, but my experience with them has been that they are very heavy and very dense and I had to add some peat, leaf mould, and sand to them to get my plants to thrive. Honestly, any general purpose potting soil would work, so you could buy whatever is on sale. If you get a soil that does not contain fertilizer, buy a small packet of time release fertilizer for vegetables and use it according to the package directions.
If you are apt to forget to water frequently, it's worth the extra money to invest in the slightly more expensive potting soils that also have a moisture control polymer added in. You can also buy it separately - look for a product called SoilMoist and add a tablespoon full under the roots when you plant the peppers. This stuff holds a tremendous amount of water that it only releases if the plant needs it. It has saved my houseplants from chronic neglect bit most importantly, last summer when we had a drought and water ban, our gardens did very well with the little water they got thanks to SoilMoist.
You can start seeds your best bet is to start them in the little peat pots) or buy a flat of pepper plants already sprouted. You should be able to find them at your garden center. A flat of 6 plants is less than $2. Even K-Mart and Wal-Mart sell them.
If you plant them in potting soil with timed release fertilizer, you don't need to add any additional fertilizer. Just keep them well watered. When you plant, be sure to use a large enough pot, and add some pebbles and sand (I often use that Styrofoam popcorn that comes in packages) in the bottom so that you will get good drainage.
They need sun but they also need some protection as the stems are fragile at first and easily damaged by wind, and sun that is too hot will scorch them. If you have a patio that gets bright sun, place them close to the house so they get protection from extreme heat/sun.
It's almost impossible to grow them successfully indoors - you can grow lovely plants that will produce blossoms, but peppers need insects to pollinate the blossoms so the pots do need to be outside where bees and other pollinators can get to them. Even if all you have is a small balcony or patio, or just a front stoop, that is adequate for bees and other beneficial insects to be able to pollinate your peppers.
I don't know where you live, but peppers can be fussy if the temperatures are too hot - they might not set fruit if you happen to be having a heat wave when they are pollinated. You can Google the particular type of pepper you grow for more detailed information.
Enjoy your peppers!