The Saiyuki Anime Watching order

If based on the time-base events in the anime

1. Saiyuki Gaiden
2. Gensomaden Saiyuki
3. Saiyuki Reload
4. Saiyuki Reload Gunlock

If its based on when it was shown/created, Gensomaden Saiyuki is first.
Best to watch Gensomaden Saiyuki first.
My order was 2341 since I only discovered Saiyuki Gaiden last.

 

Saiyuki Gaiden's animation is amazing, but the actual series' is pretty bad and doesn't follow the manga accurately after about 10 or so episodes. If you haven't read it first, you may be confused. Plus the manga is superior to the anime. The only thing I like about the anime is the japanese voice cast, which is awesome. The dub is horrible. I highly suggest the manga over the show.

The movie is good too though if you ever wanted to see it. It's called Saiyuki: Requiem. It takes place during Gensomaden Saiyuki.