Hey there.
Well....I would highly recommend both, but if you had to choose one at the moment, I would say Cowboy Bebop. Very good series and is a definite "must-see". The plot is solid, the characters are
excellent, the music is superb, the comedy is classy, and it's just overall great. However, I must warn you....if you're very emotional, this series is dramatic. Just to prepare you. I hope this helps.
As for Trigun, the same thing applies.....the plot is dramatic but good, the characters are also
excellent, the music is awesome, and the comedy...while not very much in the later episodes, is still very humorous. I'd say get this second because while the plot is terrific, it's not "wanting to see the next episode right away" terrific. At least IMO. You may think differently. I hope this helps too.