I have no experience with the kit you link to, but at $70 it's probably a decent place to start. Usually the cheap stuff is difficult to work with — slow to set up and fussy to adjust — and of course it's not as robust as "pro" gear. But with patience you can get first-class results from almost any light modifier.
One possible gotcha could be the light stands, which aren't very tall at 7 ft. Around 8 ft or more is better for lighting a standing adult's face. If you're shooting a group of people you'll need a decent height for more flattering light on the faces. The umbrellas are also pretty small, so you'll have to place them close to the subject to get soft light. None of this is a problem if you just want to light small items on a tabletop, of course!
If you think you'll need more power, and would enjoy using a softbox, have a look at this Interfit kit
(with two monolights, which are self-contained lights like a huge Speedlight that you plug into the mains). Interfit is a good, solid brand for all kinds of low-cost lighting stuff. Check their products on B&H, etc.
By the way, you can do a lot with one light, such as your existing Speedlite, and a carefully placed reflector (something like this
might be a good place to start). Two lights can give the inexperienced enough rope to hang themselves, whereas one light and a reflector is more similar to natural sunlight, and therefore, easier to get natural-looking results from.
For a readable textbook on photographic lighting, choose Light — Science & Magic
. This renowned book is especially useful if you're technically inclined and you plan to light things other than human beings. It goes into great detail on how to make metal look like metal, leather like leather, glass like glass, etc. It also very clearly explains concepts like the inverse-square law and the "family of angles" — things you need to know to reliably get good results.
A good online resource for lighting generally is David Hobby's Strobist blog
. Hobby started out using off-camera Speedlights with cheap modifiers, though I think he now uses full-on Profoto
stuff (expensive, heavy, powerful). But he still talks engagingly about all kinds of photographic lighting.