If you want a great into to Stargate the Stargate movie is a great place to start. Next you would want to watch SG1, which dives even deeper into how the Stargate works and the different races of the universe.
At the end of season 7, if you want a bit of a change and a break from SG1, Stargate: Atlantis is introduced and is a great off shoot. The cast is awesome!
After that watch the rest of SG1, and the other 2 movies (Ark of Truth and Continuum)… as for Stargate Universe and Origins… Origins can be watched whenever. Universe can be watched last or not at all… in my opinion it was the worst series, very boring and too over dramatic.
Have fun watching!!