There are many rendered and real-time ways to create animations of particles. The easiest... maybe... is After Effects and the various plugins that create different kinds of particle animations.
But, given that you're going to be paying big money for the plugins that make the best particles within After Effects, and that the workflow is often painful without realtime, I'd strongly suggest the following:
Learn/try/master Unreal Engine 4. It has an amazing particle engine.
Truly very good, easily the best in class. And comes with free, ready to use, basic examples, e.g.
AND can export individual frames with alpha information, with ease.
PLUS you can vastly overload your system's power and set it to do very complex render passes as frame by frame .png exports, meaning you don't need to use any other software.
Unreal Engine is, very truly, a work of art, and a tool beyond compare.
And the community and help you can get from it is second to none.
Far further down the tree, but perhaps a little easier to use (much less features, though, and vastly inferior rendering quality) is the Unity game engine. It's a little trickier to figure out good exporting of individual frames with Unity, though. And it's really not fun when trying to do more complex particle effects. But if your needs are simple, this will be sufficient.
And all the necessary, good features of Unity sit behind a paywall. No other word for it. They're a bit cynical in the way they treat their "customers".