Rent your signature like you are doing right now, and start with YoBit, C-Cex, Poloniex or Cryptopia. Sites that you can buy altcoins with a minimum of 10.000 Satoshis, por example.
Before buying a coins, read the thread of the coins, what the people think and of course if you think that coin has future. If that's true, the price will go to the moon. But not buy, just for buy...