Softbox vs Umbrella
I am often asked which modifier is the best to start with and I can never give a straight answer. It depends on a lot of factors and I believe you should never rush into a purchase or buy something just because so-and-so uses it. Find out what will be the best option for you and your specific needs.
However, I generally recommend a softbox or umbrella as a good starting point.
The Umbrella
An umbrella is a great modifier to start with as it is a super affordable option. It will give you soft beautiful light that can be used in many different ways.
The image below is lit with a shoot-thru umbrella. The light is soft and pleasant but you can see quite a bit of light spill onto the surrounding area.
The Softbox
The light quality from a softbox is very similar to the umbrella but you will have more control over the spill and angle of the light, especially if you purchase a grid to go along with the softbox.
A softbox will normally be more expensive than an umbrella and it comes in a wide variety of shapes and sizes.
For the image below I used a square softbox that allows me to control how the light falls on the background. This works well for my style of shooting as I like things dark. You do not have to use the softbox in this way, you can create a brighter image by your light placement and settings.
Here are a few examples of the light quality you can get from a variety of modifiers using the same setup:
And some real-world examples:
Please let me know if you have any further questions!