I am a newbie at this and yesterday I installed Win 8.1 x64 so I would like to use the most suitable program for making my tasks in C/C++. Thanks
MinGW supports only 32 bit binaries, TDM supports 32 and 64 bit binaries (with usage of MinGW's API's).
Both released GCC 4.8 approximately at the same time, so there's no real difference in up-to-dateness.
My recommendation: Use the 3rd alternative: MinGW-w64 instead - it's a extended MinGW with support for 64 Bit. See here for a short description of MinGW-w64.
Whatever choice you make, better use official developers website for downloading (not Orwell's) to get most up-to-date version.
Btw., you'll find a good overview there, what makes one special about the others.
NB: the homepage of mingw-w64 used to be on sourceforge but is now at http://mingw-w64.org ; links have been updated accordingly.