When you select avocados, you should make sure they are firm and slightly soft, with no cracks and sunken spots (they tend to oxidize, become dark, and possibly spoil the oil, and at the very least they alter its taste making it bitter).
A sign of quality is the presence of a slight neck at the top (instead of just being rounded), since this means the fruit probably ripened on the tree, which usually ensures a better flavor.
Avocados can also be ripened at home if they're less mature.
A brief overview of California avocados: Hass avocados usually weigh 250gr (around 8 ounces), with a pebbled dark green skin (sometimes very dark), while Fuerte avocados have a bright green skin, which is also usually smoother: try to avoid Fuertes with a skin that's too bright though, since their flavor isn't the best.
Florida avocados are usually larger (they can reach 4.5 pounds in weight) but generally have a lower caloric density and a milder flavor (due to their increased percentage of water).
Avocados can be ripened at home: it'll take a few days, at room temperature, and you can check the process since their skin turns darker as they ripen.
Don't refrigerate them before they are ripe, since cold temperatures stop the ripening process.
Once ripe, avocados can be stored in the refrigerator (they keep for longer when whole, so don't slice them if you don't have to:this prevents their flesh from turning brown), where they'll keep for a week.
If you have already sliced it, a good trick consists of sprinkling lemon juice on the exposed parts of the flesh, to reduce oxidation, and then storing the remainder of the avocado in the refrigerator, wrapped in plastic wrap or inside a plastic bag.