Given that the original League was Mina Harker, the Invisible Man, Allan Quatermain, Jekyll/Hyde and Captain Nemo, the schtick is obvious. Pick a time period, and assemble 5-7 heroes of that time to be the League of that era. Don't worry about duplicates, it's all for fun and game ideas.
Anyone suggesting a 1980's League without MacGyver will be ridiculed.