Switch to animate or stick with after effects

Character Animator is amazing for lip sync, head and eye movements.  After Effects makes videos and you can do a lot with it, but you do have to set up limbs etc...  Animate used to be called Flash (oh man, i miss Flash) and you're right, it can be used to make simple, low file size animations, but the video export element was added later.

You might want to look into adding the free DUIK plugin which can manage your inverse kinematics for you (limb movement) and possibly Bodymovin - which can let you export animations to code.

The most control you'll have is in AE and if you are sticking with video export, you can replicate all the features of Animate in AE (I'm thinking here about looping sprites, those are the same as precomps with time remapping set to loop).  Character Animator gives you features not in the other two, but I use it to generate my avatar's lip syncs, which I can then import into After Effects.

Animate is a very good tool for web-based animations. Character Animation for a movie is usually a little more complex. If all you need is simple, Animate may be a good way to go. My friends that do a lot of Character Animation have mostly moved to 3D apps. Blender is an amazing open source, which means it is a free tool. I use it more often than Cinema 4D for modeling and animation because I started learning 3D modeling with Blender and know where all the tools are hidden. That will be a great starting point if you want to get into more sophisticated animation.

If you have or want to develop some great drawing skills, you can look at Moho Pro for Mac, CelAction2D for Windows, or the one I tinker with, Procreate for iPad. I think there is something similar available for other tablets.

Whatever platform you use to create your animations, if you want to make a movie, do what the pros, Pixar, Disney, and all the rest do. Each shot is a separate project that you start by planning and visualizing with a pencil sketch (rough preview of the timing, composition, and blocking (how the characters move). When the Pencil Sketch works, move on to Ink and Paint, which is polishing, full color, effects, backgrounds, and anything else you need to do to finalize the shot. When the Pencil Sketch and the Ink and Paint (industry terms that are about 100 years old) are done, Render the shots. When you get all your shots rendered, edit them, and do the final sound mix and color correction in an NLE like Premiere Pro, Davinci, Final Cut Pro, or even Movie Maker. Nobody has the skill or patience to create an excellent animated movie in a single composition that lasts longer than a minute or two. I used to create a lot of TV commercials in After Effects, and most of them had at least a half-dozen AE Comps in 30 seconds.