the videocard is fine (at least for league).
8gb of ram is fine for league.
the processor is fine for league.
its not that its a bad computer, but for the money you could have done better building your own.
I wouldn't worry, you'll be able to play league on max settings.
if you don't have a gaming monitor with more than 60hz refresh rate, just lock the fps. there is nothing to be gained from having high fps, if your monitor can not display it!
in the future (and i'd do that sooner than later, add a ssd and use a migration software to transfer your c drive to that ssd. (samsung are market leader, and the evos with nand have a 5 year warranty)
Your computer also allows max 16gb ram.
find out your rams mhz speed (1333 or 1600 usually) and then look out for good sales to get an additional two 4gb sticks (always buy a pair), maybe next black friday. Preferably buy exactly the same brand and model of ram that is already in your computer.
The gtx 750 is a budget card, but hey, you didnt pay top $ on the system. its gonna suit your needs!
and in case you are afraid touching your machine: Hard drive and ram updates do not void the warranty.