Focus on one art first, then once you think you have got it, you can start another while continuing the previous. Now for art, their is no BEST, one person may be good for BJJ, but another person may be better for Judo. For grappling, I personally love BJJ(expect a lot of rugburns and cuts if you are new to grappling). If you look into the history, you will learn it is basically an improved version of Jujutsu.
However, so is Judo. Judo focuses more on throws and has some grappling as well, but not nearly as much as BJJ. I have also heard it is harder to adapt into no- gi fighting. For striking, muay thai is good, but so is boxing, kickboxing, and even Karate. I say "even" because even though it is more traditional, many people use karate as a base in their striking.
Personally though, I like the BJJ, Muay Thai combo. Its the one I use. However, I have also taken a little Judo, kickboxing, boxing, and TKD as well. I use my combo for MMA.