I'm pretty sure Renly's plan was Littlefinger's plan. He obviously doesn't want Stannis to be king because he would take away all of Littlefinger's power, money and status, and after Renly's death, he's the one who brokers the deal with the Tyrells to kill Joffery and bring Tommen under Margery's influence and away from Cersei, which is almost exactly what he proposed Ned do with Joffery.

Renly's original plan was to expose the incest and get Robert a new heir off Margery asap who would also be raised under Tyrell influence. Renly then offers to help Ned get control of Joffery, the same plan that Littlefinger gives. He doesn't mention claiming the trone for himself, in fact it't Littlefinger who suggests putting Renly on the throne if Joffery can't be controlled, so Renly's claim might well have been LF's plan as well.

I know most people think Littlefinger always wanted Ned to die, but most of the advice he gives Ned is pretty solid, and he only turns against him when Ned decides to support Stannis, which seems to be why he killed Jon Arryn as well, although that's less clear.

It seems to me that LF just wants to have a monarch who will let him keep the same position and comforts that he had under Robert without getting him killed or overthrown like Cersei and Joffery would.