3D design

for game design you start by picking a engine to run your game;

Mac users = Unity as that is really the only thing that still runs on a Mac

Windows users = most people start with Unreal engine because like Unity these are free

if you have money to spend and want software that holds your hand a bit more there is Iclone but its $$$ and aimed more at making animation i.e, like the movie bit at the start of the Mass effect games

for models you need a true 3D software like Photoshop, Maya and Blender... I use Photoshop for 90% of my model making and Blender for the rest but its old and people starting now are better off to learn Blender first because its free but also because its more up to date then Photoshop or Maya

most schools will want to teach you Maya because (back in the day) that was the standard and to be fare it still can do a lot but you really are better to learn Blender

Those are the basics then you pick what part of game design you want to learn i.e, do you make the story, the code, the models etc most people try to learn at least a bit of everything but you will have one or two things that call to you more than others and that is the best way to start i.e, do what you like best