Your copies will work on some, not all, DVD-Players. Of the two formats, DVD-R(W) is more compatible than DVD+R(W)(At least for the time being), and, as such, would be recommended for standalone playback.
You really should get a General Use drive, since the discs are cheaper, have a higher capacity, and are the ones intended for home use (The authoring ones are aimed towards content-creation from what I understand).
If you’re going towards writing for use in a standalone, I’d recommend the Pioneer DVR-A04, for good performance, good build, and being a DVD-RW (As opposed to the Philips/HP/some others DVD+RW).
The war between these two competing formats really makes the choice a difficult one to make, and complicated too. There were some problems with DVD+RW, and I’d say that DVD-RW is a more “estabilished” format, but, remember, there is no set standard yet, so walk carefully!