In order, there is the OVA, called Techi Muyo Ryo-Ohki, and then there is the TV series, called Tenchi Universe, and last there is the Tenchi In Tokyo.
Ryo-Ohki is the OVA and is 20 episodes long, and it has separate arcs. Tenchi Universe is a more drawn out 26 episode long series based on the first arc of the OVA, very much an alternate retelling. Tenchi Universe is what most people are familiar with. Tenchi in Tokyo is an entirely different story and you really don't need to worry about that, trust me, that's not the one you're looking for. There are also two spinoffs, Tenchi Muyo GXP and Pretty Sammy, but you're not looking for them either.
I recommend you get Tenchi Universe. The series is a journey, it's fun, and it's hilarious. It's characters alone are worth it. I admit that the main reason I like Tenchi Universe so much is because of the characters; they have so much personality and watching them in the episodes and interacting with each other is oh so entertaining.