Do I need to watch the other Stargate series

You don't need to, it is possible to watch this without watching any of the earlier Stargate productions and have a general idea what's going on, only because they give a very basic info dump of what it's all about.

However, you would benefit from watching the other stuff first, they'll fill in the blanks, and much more that happens in SGU will make a lot more since.

I'd say watch them in order:
Stargate (1994 movie)
Stargate SG-1, seasons 1-10
SG1's The Ark of Truth
SG1's Continuum
Stargate Atlantis, seasons 1-5
Stargate Universe, seasons 1-2

The other Stargate series and movies will give you more background on certain characters and on how the Stargate works. Start with the 1994 movie.

If it's all the same to you, I'll have that drink now.-Loki (Marvel's Avengers)