Some cycling jackets come with hoods, some don’t. This is a matter of personal preference and what kind of riding you do. A hood may be great for an exposed rainy MTB ride, but might obstruct your peripheral vision if you are using it on your urban commute. It can also be hard to get one that fits comfortably under a helmet.
The best of both worlds is a jacket with a removable hood, or one that can be packed into the neckline.
Pockets are always handy. You’ll tend to find that you get side pockets more commonly on entry level and MTB jackets, and race cut and road jackets may have them on the back of the jacket or not at all.
Some jackets also have a mesh or fleece lining. This is a good news for comfort, as the inside of a jacket can feel cold and plastic-y on the skin. It also means some extra warmth and insulation. On the downside, it makes the jacket heavier and bulkier.
You can also get packable jackets, which are designed to crumple up to a small size so they can be carried easily in the bottom of a bag or in a jersey pocket, in case of unexpected rain. At the higher end of the price scale, you can find some very highly rated waterproof jackets that pack down very small indeed, like the Gore Alp-X jacket.