Hi Unique User,
I am just beginning on the adventure of travel hacking / churning (4 months in). The common advice is to get a Chase Sapphire Reserve card as one of your first. As you are pushing into the 5/24 range, I would definitely suggest Chase before they are gone from the realm of possibilities. Chase partners with United which flies down to Lima and can connect with you to Cusco if that is the plan.
I am personally valuing the southwest companion pass rather highly and working on a couple of cards to earn it but Southwest doesn't fly down there so steer clear.
Good luck and let us know how it goes! Peru is great!!