If you're not going to watch the whole lot, just skip SG-1. "Lost City" is great, but it comes at the end of an arc and has a different (and better?) actress as Weir. "New Order I and II" introduces the new Weir actress, and takes place right before the Atlantis pilot...but it also comes in the middle of an arc. "48 Hours" and "Redemption I and II" are the SG-1 episodes that feature McKay (the ones before Atlantis started, anyhow), but they also come in the middle of other storylines.
You'll get to know all of these characters in short order on Atlantis, and any references to SG-1 will be small, or explained.
Personally, SG-1 is a far better series than Atlantis (especially the latter seasons of Atlantis), but if you're just going to watch the spin-off, don't bother with SG-1. Too confusing keeping things straight when you're only seeing a few of the puzzle pieces.