One thing I found starting out was that my hands were not happy biking. So, in fairly short order, I picked up bike gloves. Gloves are there to do several things. First, they protect your skin from abrasion. Second, they often contain padding intended to prevent you from putting too much pressure on nerve channels (although they often times fail at it) and also to provide cushioning from vibrations. Third, gloves usually have a strip of absorbent fabric for you to wipe your sweat with. Fourth, gloves designed for cold weather will keep your hands warm.
Cyclists tend to prefer fingerless gloves most of the time, unless it's really cold out. I usually switch between a pair of light full-fingered gloves and fingerless gloves, although there are thicker full-fingered gloves for the winter.
There are a lot of brands and you really need to try them on in the store with your bike to know for sure. They don't need to preserve a full range of motion, so they might feel a little weird if you wear them all the time but then feel right on the bike.
I'll put this under "bike-specific" because you don't see them so often elsewhere.
Because you are generally wearing a helmet and need an ability to look side-to-side, hoods are far from ideal for biking. Instead, there's the Balaclava, which is designed to fit around your head and neck. It keeps your head from getting quite as cold or wet as it would otherwise. But it also doesn't get in the way like a hood will.
Sunglasses are pretty much optional. Your eyes are perfectly able to deal with all sorts of different lighting situations on their own. Otherwise, we'd have been born with sunglasses. However, I've found, especially in rainy and cold weather, you want something akin to sunglasses to keep the cold wind from drying out your eyeballs or the water from splatting right in your eyes.
The problem with most normal sunglasses is that they are designed for drivers or pilots or people on the beach who are not working out. Eventually, sports-oriented glasses came about. The trick is that you have to let a little bit of air through so that they don't sweat up. There are also water-repelling coatings on higher-end glasses.
And, because you might be riding in dark-and-rainy weather instead of bright-and-sunny weather, they are often either offered with interchangeable lenses or with photochromic lenses that darken in response to sun. The advantage of photochromic lenses is that you don't need to swap lenses when the light changes. However, I haven't seen any photochromic lenses that I'd consider to be safe for use at night.. they never get really transparent, so I prefer interchangable lenses. After a while, I realized that I actually prefer to leave the clear lenses mounted all of the time. They still absorb harmful UV from the sun, but there's just not enough objectionable glare around where I live.
You can also get somewhat tinted lenses that will absorb more of the less useful wavelengths of light and less of the wavelengths of light you need. I actually prefer them to the non-tinted version, it's just that I have to take them off if I want to take pictures.