Im not sure if there is a minimum one needs to invest if pursuing that path. But i was thinking of sticking to my ZEC mine and drop 100$ into buying ETH every two weeks.
Current ZEC price now around $470 based on CMC stats. Feb 7, that was the very low price of this ZEC reach the bottom $300 and now price going increasing fast only took 1 week it has reach $500. So, i think it's very worth to invest on, it's good speculation to buying on every two weeks will get your good return profit in few month later.