There are a few things to consider here, the first being what kind of animation do you want to pursue? There's 3D animation which is where you move 3D models across multiple images on a computer to animate, 2D animation where you'll use drawings as the images to convey motion, and stop motion where you craft a real puppet using materials sturdy enough to be moved and a flexible skeleton inside and use a camera to take images over time. There are other types of animation in between these but these are the main three. Each has a different consideration to take into account so each requires different software. My recommendation is Maya for 3D, Toon Boom Harmony for 2D, And Dragon Frame for stop motion these are the industry-standard software. However, this software tends to be very expensive and as such may not be fully accessible to everyone so it's always a good idea to get a student license version of the software if you can since they offer a discount or even can offer it for free. If you were going to the indie route of producing your own content outside of the studio environment and wanted to use software that works on a tight budget I would recommend Blender for 3D / 2D and Krita for 2D. These are open-source software available for use by individuals for free so they are very budget friendly. I don't know of any open-source stop motion software however a quick google search should provide some software to try.
I hope this helps