A contrast resulting from umbrella and a point light source (such as halogen lamp, which I love so much) is easy to control. Silver umbrella gives the harshest light, but it's still soft enough - next comes the white bounce, and white shoot-through. I like to use white bouce umbrella as a fill light, or as a main light in high key - the shot-through umbrellas are good to light up the interiors, pictures and macro objects. It's easy to fine-tune the contrast of the light with umbrella by adjusting its position relative to the lamp - as with the spot. I don't own a softbox because I mostly use hot lights - umbrellas just don't overheat so much. Also, round reflections in the eyes and other shiny objects are quite more pleasing compared to squares
But the options are endless - if I want to recreate a sobtbox look, I use a shoot-through litedisk, a small 50cm one. And it has no sections to show on my pictures, BTW - I can place it closer if I need.
Cheaper umbrellas will work with flashes, on my opinion - where the light comes in bursts. With hot lights the cheapos would either yellow or melt down
I have Kaiser and Hensel umbrellas, and they work without a flaw - a white combined, and silver one. When you buy one, look for more sections in it (say, 10 is fine) and for overall crafting such as the cloth put together with wires by a real thread. Also you should check the metallization of your umbrella (if it's silver or gold) - you should not be able to see anything through the metallic cloth!
Cheers,
Zhenya