Tripods
The heavier the better. The fewer leg joints, the better. Avoid using the center column. You get what you pay for.
If you have more than one leg joint, and you're not extending the legs all the way, make sure that the smallest diameter leg section uses the least extension. This gives better stability.
When it is getting dark.
You need to use a tripod when your shutter speed is slower than 1/focal-length of the lens. Thus with a standard 50mm lens, you should not attempt to handhold shutter speeds slower than 1/60th and with a 500mm telephoto lens, you will have to keep the shutter speed at 1/500th or faster. Rationale? Longer lenses magnify the subject but they also magnify any vibration of the camera.
If you were really serious, you'd use a wooden tripod. "Wood absorbs vibration and metal transmits/reflects it," is how the view camera perfectionists put it. However, the user interface and flexibility of wood tripods is so poor that only a few diehards are able to resist the charms of metal legsets.
Make sure that whatever you get, it is tall enough that you can use it comfortably without extending the center column. Think about it: if you raise the center column, your camera is flapping around in the breeze supported by only one tube. If you push it down, you get your camera supported by three legs as advertised.
Two companies make the vast majority of legsets used by professionals, Gitzo and Bogen (Manfrotto outside the U.S.). Both brands offer adjustable leg angle, which is nice for uneven ground, slopes, and resting a leg on an overlook barrier. Both also offer reversible center columns, for hanging the camera inches from the ground.
Monopods
Sports photographers often use a monopod so that they don't have to support the weight of a 300/2.8 or 600/4 lens through an entire football game.
If you are doing architecture, you want a three-way panhead in which each axis is separately controlled. Otherwise, you'll probably find a ballhead vastly more convenient.