Parties? No. I personally am a Marxist-Leninist, which is the most common example of Marxism in practice. I would say that speaks to its practicality and relevance. If I were you, I would read my reading list (or another comparable ML focused reading list) before joining a party or org, then feeling out local orgs for yourself.

Trots are a strain of Marxism, just like Marxist-Leninists, so there are many groups that adopt either tendency. There are also Maoists, Marxist-Leninist-Maoists, and many other tendencies, so the best thing you can do is read theory, discover what tendency you align with, and find an org that fits that.

My personal bias is, again, Marxism-Leninism, and here's my guide again for quick access. Let me know if you have any specific questions!