how deep into rigging I have to be to start learning animation?

Sauron

Probably the question you animators get asked a lot, but!
 Many years ago when I got started with 3d I did it because I wanted to be an animator, and I made it through a couple of tutorials, got known with the toolset 3dsmax was able to provide. Then I wanted models to actually animate and went too deep into modelling. And in pursuit of better tools for a modeller I started to use maya, and now im super comfortable with it and cant stand max. And Mayan animation side is absolute darkness for me, I never used a single tool aside from parenting a grouping probably.
 So from my 3dsmax animation days I remeber I started from rigging and only then I went into animation and tutorials I was going through actually stated that it was REALLY important to do in this order, it was probably 10 years ago, so was pretty hard to get your hands on community rigs and stuff, right? 

Actual question is how much about maya rigging and rigging/animation tools do I need to comfortably start learning animations and if there is a good course/tutorials that will satisfy my needs? And yes, I prefer maya, even though I have no idea which one is better in this case

Thanks!

AnthonyAnimation

Zero. You don't need to learn any rigging to get started with animation. It's good to eventually know some rigging, but if you want to be an animator it's more important to learn to animate. Like you said, there are plenty of free rigs to use. Animation takes a long time to learn and get good at. I would recommend solely learning animation until you're comfortable enough.

If there are models you'd like rigged there are always auto-riggers like Rapid Rig Machine or Advanced Skeleton you can use for free.

tyree

you should look into cat for 3d max. it was made by animator began as a plugin. 3d max owns it now. comes with 3d max. you can rig any model in 5 minutes regardless of how unorthodox the model is.  sculpting programs allow someone that cant model a box to make anything they want. cat did the same for rigging and animation. animation is actually enjoyable instead of just technical

Hito

depends on what you mean by "rigging"

You should know how to build a skeleton and skin weighting. you don't have to know how to  build a full featured animation control rig, but having basic knowledge of the standard types of constraints is very useful. If you just want to animate there are plenty of free and low cost rigs in the Community Rigs thread. Mostly for Maya, a few Max rig in there as well.

rigging plugins handles skeleton and control rig for the most part, and can give you a solid 1st pass skin weighting to build on.

in Maya you have a lot of options,

free:

Human IK is built-in, mostly intended for humanoid characters, but possible to use for creatures

UE4 Animation Rigging Tools, game oriented, good for humans. maybe possible for creatures (probably not easy)

dpAutoRigSystem, don't know much about it, but free, and looks pretty flexible

not free:

Rapid Rig, a human focused flavor and a general flavor good for humans to any kind of creatures.

Advanced Skeleton, pretty generalized, good for human and any kind of creatures

Anzovin Studios Setup Machine 3, don't know much about it, comes in standard and game oriented flavors

Rmunday

Piggy backing off what @Hito said, If you want to make your own rigs but not have to delve into advanced techniques I  cannot recommend Rapid Rig Modular enough. It has amazing built in features, if you can find a model online you can rig it up with Rapid Rig. Human, creature or even some basic/moderate machines. All of that for a bargain price as well.

If you are wanting to animate focus on animation, technical animation is its own discipline that requires just as much effort and input to learn. There is no shortage of awesome free and paid rigs. A lot of the free ones are fully fledged rigs with amazing features.