It really all depends upon how you want to go about getting into torrents. Like Neatname said you could go the public route and just use TPB, Kickass, etc. But, that's not the safest option by any means and I'm not sure what kind of pre-times they have on public trackers and the backlog is limited at best.
For private trackers you either need to manage a ratio of upload/download normally, but some sites offer a bonus point system or are completely free-leech (you'll just need to maintain seeding a newly downloaded torrent for x weeks).
As for specialized trackers for movies/tv shows/games/etc you definitely don't need to start off that way but specialized sites are awesome if you want anything older. Getting into 0-day/General trackers should be a pretty simple task. There's BaconBits (over at /r/baconbits), SceneAccess, TorrentShack (Which is freeleech), TorrentLeech, and a ton of others. You can always checkout /r/opensignups to see who has open sign-ups.
General trackers will help you out for all the newer movies, TV shows, games, etc. What you find on TPB/Kickass you should be able to find them there as well. But, on the plus side a private tracker is also going to have more moderation than the completely open trackers. The uploaders are normally limited in number but their releases are almost never mislabeled/buggy/virus ridden/etc and at least for a while there's enough seedbox owners to give you pretty fast speed for any of the newer things.
Private trackers are awesome when you're looking for older shows/movies/etc. For TV shows there's sites like: BTN (probably the best around), FreshOn/TVTorrents, BitMeTV. If you're looking for an older TV show that was not too popular or never put on DVD you might be able to find it over there. On a public site the seeders are normally dwindling or non-existent at best. With the bonus system BTN has built around most of the obscure stuff still remains seeded for a long time.
For movies you have sites that cater to high definition releases, so if you truly care about the bitrate/quality of the releases you can join up somewhere like AHD. There's also PTP which is basically the BTN of movies. Extremely old and rare movies are in large numbers over there. They also have a bonus point system and a very lax ratio requirement that keeps even the most obscure of movies seeded for a long period of time.
Torrenting for music is basically a split of What and Waffles, What having the larger content base but Waffles is a little easier to maintain a ratio. You'll probably be able to find the most recent albums/maybe some larger bands older stuff but for music you pretty much need a specialized tracker unfortunately. But they're not hard to get into and you should be able to get an interview at one of them pretty quickly.
Depending upon how much you intend on downloading you may need to look at getting a seedbox to help you build/maintain a ratio. Many private sites offer freeleech torrents pretty frequently so if you have a fast upload connection you should be find to hop on those immediately and start building a solid upload amount, if not for a few dollars a month you can rent a seedbox that has a fast connection and can seed things for you. There's tons of them around at varying price-points. If you consider going this route, you can checkout /r/seedboxes for some more info.
If you're looking at getting into complete automation: CouchPotato (for movies) is setup for some private trackers as well as public trackers. SickRage and Sonarr (for TV shows) work well with private and public trackers as well. Headphones works okay with both What and Waffles, but I find music to be easier to manage manually.