I've never cooked with peppers or chilies but I'd like to start - any suggestions?

In general, peppers that are larger in size tend more to the milder end. When pan frying, add chiles at the same time you add garlic to get that awesome flavor. Wash your hands immediately after chopping and handling chiles; that capsaicin is no joke.

if you really don't want any heat you can go with bell peppers. I think green bell peppers are vile, but orange, red, and yellow have nice flavor and color.
I agree with the Anaheim and poblano recommendation, too.
if you want to acclimate yourself to spice you can always go with a little dabaroo of hot sauce.

they sell little cans of chopped mild green chilies. a teaspoon or two added to soups or chilies or cornbread or whatever lends a nice flavor without much heat. i personally don't really like the flavor of anaheim or poblano peppers but there is a cheese stuffed poblano dish that is available at most mexican restaurants that isn't too bad you could try. for really good hot chili flavor without too much heat, make sure to remove every single single seed! (i do this with a knife, and chop small and only use a little tiny bit if you use fresh, (like a 1/4 teaspoon finely chopped jalapeno or thai volcano pepper for a three egg omelette as an example. though for even milder they sell "tamed" canned sliced jalapenos that are pretty mild with a good flavor. you can also experiment with powdered cayenne pepper, ( a little teensy bit goes a long way!) red pepper flakes, not too spicy, and louisiana hot sauce or sriracha. again if you don't like heat you'd want to just add a teensy little bit.