i signed up for Dota2 on steam how long does it take for them to decide whether or not i'm worthy to play it or not

i've been playing heroes of newerth for now (normally i'd play dota 1 on warcraft 3 but i reinstalled my OS and lost the wc3 installation discs) which is essentially just dota1 but they renamed all the items and heroes, and made all the overpowered heroes from dota1 suck ass

how does dota2 compare to dota1?
whats league of legends like?

i'm just trying to find something interesting right now to ignore the fact that my brain is basically fried at the moment; if i can distract myself with something interesting it helps my brain heal faster or something it seems like