Ok tenchie muyo
what do I start with?
It's .... complicated .... as I understand it ...
(1) 3 OVAs comprising 20(?) episodes ...
-The first OVA is episodes 1-6.
-Episode 7 is a special.
-Episodes 8-13 are OVA 2. (Including the bonus episode 13.5)
-Episodes 14-19 are OVA 3.
-Episode 20 is a special.
The OVAs are also known as Tenchi-Muyo Ryo-Ohki
(2) Continuity wise Tenchi-Muyo GXP follows (1) about a year after the third OVA
(3) Tenchi Universe ... TV remake of the first 6 episode OVA + Mihoshi special (with quite a few changes)
(4) Tenchi in Tokyo ... reboot of the franchise
(5) The movies fit in:
Daughter of Darkness - after OVA 1
... in Love - After Universe
... Forever - After ... in Love
(1), (3) and (4) are separate timelines. There are also various spin-offs as well (Magical Girl Pretty Sammy, Sasami: Magical Girls Club).
Personally ... I'd say go with the original OVAs (Ryo-Ohki) followed by GXP. I seem to remember enjoying GXP the most of all the Tenchi properties, (athough I can't remember Universe at all, although I know I've watched it, and I'm pretty sure that Tenchi in Tokyo is still in my backlog). I'm pretty sure I've watched it in the wrong order several times (I'm 99% sure I saw the movies before anything else for a start).
edit: having gone to have a look at my shelves actually I think my preference was Ryo-Ohki instead of GXP ... and I seem to have two copies of the OVAs, one a brick of the OVAs plus the Mihoshi special and the other a nice tin which is titled as "Tenchi Muyo Ryo-Ohki" ...