Hmmm, well. That depends on the application.
Pistols against unarmored targets? 9mm strikes a nice balance of range effectiveness and low recoil so you can get repeated strikes on target, your specific platform for the bullet matters relatively little. The Sig Sauer P226 is a popular one on the higher end. If you want to add some extra killing power, RIP rounds should help you there. Yes, those are a real thing.
Pistols against armored/hard targets? Not the greatest choice of weapon for the job, but a .460 S&W Magnum, specifically made for the S&W Model 460, is probably your best bet. One of the highest velocity and highest grain bullets you can put in a pistol platform. Look out for that recoil, though, it's not very nice.
Rifles against unarmored or lightly armored targets? 5.56 is a pretty ideal round due to its high velocity and small size granting it an impressive hydrostatic shock, creating quite a decent amount of explosive force upon impact with a soft, fleshy target and doing catastrophic internal damage. Platform matters relatively little here as well, as is true in most cases. Obviously the AR15 is a popular one for this.
Rifles against armored or hardened targets? .30-06 is pretty ideal for this situation if the armor isn't too thick, it's got quite a considerable muzzle velocity and a nice flat trajectory for ease of marksmanship. This was the round used in the M1 Garand. However, if the armor is thick or you're looking at firing into a vehicle or some such, then you may just want to step it up to a .50 BMG. Again, platform matters relatively little here. The Barret M82 is obviously a very well known example of a platform for this cartridge.
Just want something that will ruin anyone's day? Well then I suppose we will have to get a little flexible with what qualifies as handheld and go with the M61 Vulcan. Firing 20mm rounds at 6,000 RPM, that thing will turn a car into a twisted burning wreck in the blink of an eye. It does need a stable machine mount, however.
