If u dont buy gold, for sure u need gold to craft gems etc etc considering its your 1st character in D3. Gold farming need pickup radius to be efficient .. for that reason alone, Witch Doctor should be your choice in order to be able to use this item:
Thing of the Deep
+20 pickup radius on just 1 item
Other characters can farm gold efficiently as well for example Monk using Tempest Rush build but then u need to sacrifice 1 random roll on 3 gears to get +21 pickup radius.