If you wanna make 2d-fighting games, get either M.U.G.E.N. or FM2002. MUGEN is a program for saving up lots of characters and lots of other stuff for a fighing game. It cannot make one though since it's editable. FM2002 is easier to use than MUGEN, and you can also make games with it. To look for a site where English users use FM2002 the most, go search for 'FMHQ'.
my fav i am learning in school is unreal engine, but u gotta learn to code i, model it and wright the ai. Start with modding, like counter-strike halo2. Halo2 skinning is easy and get used to that then try wrighting ai scripts for the game u are modding. Move on to modelling with simple modelers like milkshape then move to more advanced programs. Just take your time and u can get a hold on it pretty quick
for beginnier who wants to make game without any programming skills, I recommend 3D Game Studio. It already has a game engine included.