Aseprite! I whole-heartedly recommend it, honestly most of the mileage I get out of it personally is the colour palettes it comes with (and the ease of making your own) and the wonderful tools for shading and the like within-palette, makes pixel art a pleasure :D
Hmm, I wouldn't say I have any very specific tutorial series or anything to follow (my path forward has been very haphazard), but for general tips in how to deal with animation and pixel art as a whole, this collection of little tips and tricks is fantastic and gives you a little bit of a jump start, saint11's stuf was pretty great: https://saint11.org/blog/pixel-art-tutorials/
Also as far as things to draw goes, https://twitter.com/Pixel_Dailies is a favourite of mine, gives you a new theme every day and you can always go look around at what people are posting/drawing, and you get an excuse to draw something, no need to commit to doing it every day or even to submit your work but the inspiration is pretty nice already :)
Plus it constrains you away from spending forever on things: https://bp.io/pd