I'm late to this party, but I think DRM could benefit by defining his parameters. Right now he's asking for the straight wall cartridge .357 bullet diameter or larger that will be most accurate and have the fastest velocity. Those criteria are too broad, because merely seating a bullet over the largest capacity case is the obvious solution. But he's after deer, not T. Rex.
What accuracy do you require? Less than 1 MOA? 1 MOA? 2? All these are minute of deer or better at 200 yards, even 300 yards. Yes, better accuracy is always interesting and desirable, but is it necessary?
What bullet weight do you need? Of course lighter ones can be pushed faster, but heavier ones (longer) will be more stabile and more accurate at longer ranges, but at the expense of more recoil and lesser velocity.
What velocity do do you feel you need related to the above?
Systems become unstable and less reliable when approaching their theoretical maximums.
It might help to moderate perimeters to select for, rather than ideal ones.