The main parameter in choosing light modifiers (soft boxes or umbrellas, for example) for studio strbes is the size of the modifiers. Generally for portraits, the larger the modifiers, the better. The main function of soft boxes and umbrellas is to change a small light source into a large one. This creates soft, gradual transitions between the light and dark areas on the subject, which is aesthetically pleasing for most portraits (or course, there are situations, when the rules are broken intentionally to create impact, but that is another story). In my opinion, the more the light source resembles natural window light, the better. This concerns the size of the light source, its position (height relative to the subject) and its colour temperature.
There is not a huge difference between brand name and generic soft boxes and umbrellas in terms of the quality of light, so I think it is safe to use cheaper modifiers without sacrificing the quality of the resulting photo.
A disadvantage of very large soft boxes or umbrellas is that they are very cumbersome to use outdoors. They are, essentially, sails that catch every slightest gust of wind and tend to topple over, unless the stands are weighted down with sand bags. For an outdoor shoot, I use Speedlites, preferably off-camera, triggered by a PocketWizard radio triggers.
I found that getting started with studio lights is a bit intimidating, because of the many changes in the workflow, compared to a natural light setting. The best way to start is to assist someone who knows what he/she is doing and later copy the basic setup (there is nothing complicated about it, after all). The lighting principles themselves are actually quite straightforward, and another way to approach studio lighting is to read a book, such as “Light It, Shoot It, Retouch It.”