The show lasted several years and the earlier episodes were more self-contained versus the last few seasons. If you jump into during the last few seasons, especially after the change of cast & characters (since you haven't seen it I won't say which cast members are changed ), then it'll be hard to keep up with the story lines. Plus, after the regular show ended there were several episodes that were treated as SG1 made-for-TV movies.
If you can I personally would recommend that you start all the way with movie, with James Spader & Kurt Russell, as that sets up the premise of TV show and, in particular with Spader's character, is the basis for some story lines that appear through the series for various arcs. After watching the movie, and it is a great movie, enjoy the TV shows starting at episode #1 and going one by one through them. You'll like it.
I'm a completionist, so I like to start at the beginning and watch them in order. I haven't however seen the movie. I don't think you need to. The series recaps pretty much everything you need.
In terms of just selecting random episodes, I don't think you should do that. Pick a season, (probably one of the earlier half, maybe start with 1 or 2) and then watch from there. There are points where episodes hark back to a previous episode, but there's not too many of them though.
I kept up with the tv series over the entire 10 years it was on. Recently I started missing it again so I found it online and watched the entire series over again. I enjoyed it as much this time as I did originally. After I completed SG1 I went all the way through Stargate Atlantis and loved it all over again.
Dang I miss those two series! I never liked the last one they had on and didn't keep up with it at all.
Bring back SG1, SGA and while we're at it...bring back Farscape!!!!!!!
Personally I didn't follow SGU, I watched a couple episodes and was put off by the soap opera/overly dramatized revamp and never went back. So, I don't know the answer to that question except to say that obviously I didn't care for SGU and considered what I saw of it to be a bit of sacrilege to the original SG1 and SGA.
I'm sure SGU was probably more likeable to some people than the original two but not in my tastes.
So perhaps in that is your answer...watch them all and decide for yourself.