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Basic Platformer Movement

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I'm working on a platformer similar to Banjo-Kazooie, Donkey Kong 64, Mario 64, Jak and Daxter, Ratchet and Clank, etc, and I'd like to have only basic physics in it. The physics is pretty much basic gravity (downward acceleration applied to velocity over time), some friction and some basic collision detection and response. I wouldn't be using rigid bodies. I'd be using spheres, boxes and meshes for my collision detection volumes.

 

I've also done basic collision detection like this in the past, but it can be a pain making sure everything works together sometimes. Would I benefit from a physics engine, such as Bullet 3D?

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