Please help me pick which to buy. It would help if you said why also

Can you include what lane you play/how aggressive you are in lane/your skill level?

Shaco is a jungler.
GP is a top laner/jungler.
Heimer is an AP mid that could go top lane.

^ and

Shaco is very aggressive. He almost has to counter-jungle and gank a lot to be effective.
GP can either be very aggressive with is slows and his poke, or he can play passive and Q farm for gold.
And Heimer almost can't be overtly aggressive... Unless you are very good at turret placement, he has a hard time jumping on a low health opponent and outright killing them. That said, he is good at securing an area of control and sitting back and farming.