Yeah, a strobe is much much brighter than a steady light -- so you will ned some combo of higher ISO, slower shutter speed, or wider aperture to get the same shot with a steady light that you would with a strobe. Using both in the same setup would require either turning the strobe way down (like 1/64 or 1/128... but even that might not be enough) or "dragging" the shutter (long exposure time, like 1/4 second, coupled with f/8.0 and ISO 200). I've never used steady lights, but with real studio strobes like AlienBees B800's, set up 4-6 feet away from the subject, it's not hard to get so much light that you're using f/8 or f/11, ISO 100 or even 50, 1/125s (shutter speed doesn't really matter with strobes since the strobes go off in roughly 1/5000 of a second, but you need it slow enough for your shutter to sync, which is usually 1/200 or so second on most cameras..... stopping motion isn't an issue due to the overwhelming effect of the strobe, unless you make it so much longer that ambient light starts to affect the exposure, i.e. "dragging" the shutter as described above). In other words it is like shooting outdoors on a bright sunny day.... so you can shoot low ISO, narrow aperture, and get the very highest image quality, with no DOF problems, and very sharp results even with poor lenses (f/8 to f/11 tends to be very sharp even on kit lenses).
The other thing about using strobes is that you kind of have to experiment to work out your exposure. With steady lights you can use your camera's meter to get the exposure set, like you would with natural light. Strobes, you've got to try, then tinker (either the light settings or the exposure on the camera) then try again then tinker again. Before long you'll know what settings work well together, but when you're trying something new you've got to experiment and (which I find to be part of the joy of photography). (Unless you're using all E-TTL strobes -- which I don't really recommend.)
As for a softbox vs. an umbrella -- a good softbox is designed to be very even and yes, somewhat more directional light. It's like having a north-facing window with light white curtains, or shooting on a cloudy day -- if the subject is close to the softbox (like the softbox is just out of frame, maybe 1 foot from the subject) then they will be illuminated very evenly. A shoot-through umbrella (or a cheap softbox) will show a "hot spot" where the light is stronger, and then fade out from there. One big plus of a softbox is that you can add a honeycomb grid over the front which will make the light even more directional. This is great when you want to control the light in your studio and just have it on your subject while leaving the background dark. An umbrella will pretty much diffuse the light everywhere and you will have trouble controlling the light falling on the background.