It is probably the most well-rounded sci-fi ever made. Very good characters, very funny, and the budget kept getting bigger with each season. (Probably should’ve stopped after season 8, the whole Ori plot feels tacked on - it’s still pretty solid, though.)
There are a lot of familiar actors throughout the series, including some from Trek.
You don’t need to watch the original MGM movie, it’s technically set in a different universe. But it is fun. And the events of this movie are explained in the series as needed.
Do make sure you watch the R-rated version of the series pilot (Stargate started off on HBO)
And don’t forget to watch the two TV movies set after the end of the series. One is okay, the other is excellent.
…When you’re done with that, then you can watch Stargate Atlantis which has even better characters!