The trouble with umbrellas is a total lack of control on where the light goes. I think most beginners, particularly in smaller spaces, are far better off starting out with a cheapo Chinese softbox with grid kit, something
like this. It is far easier to understand and control what is going on if you have more directional control.
For a starter kit I'd recommend two speedlites, something like
these and a trigger. They are manual only, well priced but radio triggered so no cables.
I wouldn't worry about a backdrop, after watching a million videos on YouTube you will realise you can do a lot of that with the lights.
Watch stuff like this:
http://www.youtube.com/watch?v=1WTWiN9kLts They have a huge range of very good videos.
http://www.youtube.com/watch?v=qNGiOpWEKxQ This guy has a great channel and really can use small shoot through umbrellas as well as anybody I have ever seen!
http://www.youtube.com/watch?v=91gU93J2Q8k This guy also has a fantastic range of videos and covers both white and black backgrounds with light.
And I really like this, though I'd argue the 16 looks!
http://www.youtube.com/watch?v=7zZBD6EMB1k
As for what modifiers are the best, well it totally depends on what you want to shoot and the look you want. Shoot throughs will give the broadest light, excellent for groups and real estate, reflector umbrellas will give you more control, though not much unless collapsed, but they are very versatile. Soft boxes are "best" for mood and control of what, exactly, is going to be illuminated, stylish portraits are easiest and quickest to do with a gridded softbox.