I'm no artist, but this is great for enhancing the usability of all your existing tools when peeping at pixels:

https://gumroad.com/l/glassbrick

I'd say: Go for Photoshop if you have some even far dream of getting to work at a game company. Is the standard for virtually anything. I used it professionally for making a bunch of games in 2D (pixel art), a company that created certain line of games for Nokia (2D and low pol 3D). If is the case, you wont regret it as they will ask you to master it in virtually any graphics related job. (games, web design, fashion, etc)

If the plan is never work at a company, making games is a hobby, and you plan your career by a path that would never need Photoshop -ie, not even medical jobs where even there PS is required...- then anything will do. In 3D happens a bit the same, but in pixel art, this statement is quite true: what counts is that you master the actual skill, your capabilities. As from a tech point of view, anything can put pixels, is more about your technique what counts. This is why a lot of pixel artists just use MS Paint. I wouldn't say is the majority, today. Not in companies, certainly.

So, if that's the situation, Gale will do, and has nice animation functions. MS paint is used by a bunch, but is not true what some purists say that you cannot use Photoshop to do the same. You can do with it all what MS Paint can do and a ton more.

Don't feel frightened or blocked by the excessive rigid purists that you might eventually find. Old school is nice, but don't let them force your style. Still, many of the available tutorials (techniques are very easy to transfer among all packages) have very clever procedures, done by people that know already what works best. IMO the priority here is mostly the tutorials, and use whatever software feels better for you, or Photoshop if you plan to work in the industry. Cosmigo Pro Motion is other thing I'd recommend you to learn, in that route. Personally, I don't like it, and don't use it. PS can do it all. That said,,, I have handle virtually all tools mentioned in this thread. The majority are great, rarely would go wrong with any of these.

An absolutely great tool , very young, is Krita ( krita.org ) . This one has a little few amazing features thought quite in pixel artists, but are a bit hidden, as is mainly a high resolution digital painting tool, which excels at that is its main focus. But its ability to paint seamless textures while you check how all tiles look together, the new grids and snap functions, certain attention to the pixel artist brush, show quite an intention to help pixel artists, even if as a n "extra", despite being a tool for other type of task. Still, very young... Not very usable text tool, for example, but this shouldn't matter much for pixel art. I mean, it has still its rough sides, but also extremely brilliant aspects: One of the best line stabilization I've seen to date (stuff of use for digital painting in high res, not pixel art), and a cmyk mode, very rare even in mid cost commercial tools, and krita is totally free...

If you do a lot of sprites, and is all for hobby art, go for GALE, is a great tool.

I do prefer the painting tools of Tile Studio (free), not sure if been mentioned already. A map editor with very nice pixel painting feel and UI, IMO.

http://tilestudio.sourceforge.net

But for animation, onion skin preview is quite handy for both 2d high res and pixel art. Gale has this feature.

So, a great combination is having/using both. :)

To test how you feel with an app takes one hour as much, to give several or many a nice try. What is important is that you feel confortable. If you want to buy new shoes, you only try a pair in the shop? As said, the skills are more important than the tool in pixel art. So, don't worry, you will be able to transfer your technique to whatever the tool, later on.

IMO, those are way more than enough to let you do anything you want. The key is not in the software, trust me.

There are a few other 2D animations packages, very powerful and advanced, (2D bones, meshes, etc) but not mentioning them here, as they're not really a big advantage in a pure pixel art technique. They (Spine, Dragon Bones, Spriter, all heavily used in web games, like the good old Flash, now renamed(don't quote me on this, flash is for vectors, not pixel art)) can be used for that, making use of their great UI for animation and keyframes in general, but for using them so, not really a huge advantage over using the already mentioned. For a sprite like the one you posted, I'd go for GALE and/or Tile Studio (I feel comfy with TS, not with gale. But GALE is great for animating sprites). Can be done easily with Photoshop as well, (or Paint Shop Pro, Gimp, etc) is a matter for whatever you prefer.

In the very elder Paint Shop Pro (7.x and 8.x, decades from here), not sure if they have it these days, it included a great tool, called Animation Workshop or sth like that. It was great for editing sprites, and preview animation even while drawing. It could import / export to PS in the form of a layered PSD, if I remember well.

Hope it helped,

Try this list of tools https://mobilegamegraphics.com/tools/, from beginning to the end. Also audio tools is available in there.

I'm no professional pixel artist but what I do is to draw the animation's starting frame and then the final frame. Then I either start from the first or last frame and continue to do rest of the animation.

Years back I made a small app with C++ that constantly renders and animates a set of frames in real time while I work on it in MS Paint so I could see the results immediately (well, see results after I saved it in the Paint)