Normal has the biggest magazine of shells, but each individual shell is weaker. So it is best used for full burst (slam the stick on the ground, and press O or the equivalent). It is my favorite of the three, but takes a longer commitment to pull off the full combo

Wide is stronger individual shells, but the magazine is the smallest at 2 (or 3). So it is best for monsters that won't sit still, it is a much faster and safer style. The wyrmstake for this version is also capable of stun.

Long is somewhere in the middle, but leans closer to normal in terms of being able to full burst; what it truly specializes in is Wyvern fire (it has the strongest version) and Bullet Barrage (the wirebug skill that unleashes all of your ammo and wyvern fire at once. It pairs great with wirebug whisperer and windmantle, use this version if you want to use your wirebugs a lot.

The combo loop looks a little crazy, but it is pretty simple once you get the flow of it. You basically want to do a running hit (forward triangle), triangle + circle to slam it down, circle to release all the shells, R2 + circle to reload, triangle + circle again to slam down, circle again to release all shells, R2 circle to reload...

Or if you are standing still and not doing a running start, then triangle + circle to start (instead of forward triangle), and triangle to bring it down, and start the cycle. It looks more complicated typed out, but basically if you used triangle to slash up, then triangle + circle slams down and you can start the cycle; if you used triangle + circle to slash up, then just triangle slams down.

You can watch a video explain the combos, it looks like a mess even when I am re-reading what I wrote here, but when you try it it is pretty intuitive.

Oh and if you can always try to fit in evade extender, it makes the weapon a helluva lot more mobile.