Chili Peppers

Types of Peppers

http://www.bbc.co.uk/news/uk-12505344

Types of Capsicum (Wikipedia)

Cayenne
Jalapeno
Also see Chipotle, which is a ripe, smoked Jalapeno.
Piri Piri (Peri Peri)
The African bird's-eye chili.
Scotch Bonnet
Habanero
http://en.wikipedia.org/wiki/Habanero_chili

Where to Buy

Check your local farmers market. IF you find a chili vendor who grows fresh chilis (hopefully they speak your language), speak with them about the growing season, and what other chili products they grow. You may be surprised. I've been able to acquire great products this way, and even been given invites out to the farm to pick them myself.

Your local grocer may have some. Go for the upscale ones if you're looking for unusual peppers like Habaneros.

Jalapenos generally are very low-heat when you buy them at the grocery; I'm uncertain why this trend started, but it's very disappointing. You may have to source these (or grow them) yourself in order to get a decent quality.

Specialty spice stores. Of course, you can usually find a store that caters to spice lovers in most cities.

Online! I've never tried ordering fresh peppers online but it seems possible.

Preparing and Storing

Fresh chili peppers can usually be frozen without adverse side effects.

If you have a dehydrator, you can also dry them easily.

Or, chop/slice them, and put in a squeeze bottle with oil to make your own spicy cooking oil.