In modern taxonomy Gigantopithecus is actually classified as a hominid, along with the great apes and several other extinct apes. If we're talking about close relatives of Homo, the correct term is hominins or homininans (depending on whether you include or exclude chimpanzees).
I vote Gigantopithecus because it's the best we've got right now. The size is about right (maybe on the large side), the ecology fits given certain assumptions, and there's a plausible migration path. The million dollar question of course, is whether or not Gigantopithecus was bipedal. If it wasn't, forget about it.
The homininan options are implausible and IMO not deserving of serious consideration by researchers. The first problem is height: The tallest Paranthropus specimen found to date was barely over 5 feet tall. Homo erectus maxed out around 6 feet, and aside from one disputed estimate H. heidelbergensis was in the 5' range, as were the Neanderthals. These aren't even worthy of the name "Bigfoot." Furthermore, unless paleontologists' reconstructions have grossly underestimated hair coverage, these species were nowhere near as hairy as Bigfoot was reported to be. Finally, none of these except for Paranthropus had the sagittal crest described in many Bigfoot reports.
And if you're inclined to support the authenticity of the Patterson-Gimlin film, it would seem that the homininan options listed and the film's subject are mutually exclusive.
At this point, nobody even agrees on what Meganthropus was. Paleontologists' opinions range from it being a close relative of H. erectus to it being more distantly related to us than the gorilla.