Both the 1201 and 1187 police will work for 3-gun, but neither will be optimal. Round capacity is 8 + 1 in limited and Heman class and 10 +1 for Open class. Anything under that, you'll have fun but not be competetive. Many will tell you that fast shotgunning is all about the reload. The 1201 kicks hard, probably harder than the benelli since its slightly lighter. To make it worse, sometimes you need heavier (stronger = more recoil) shells to work the action. In a game that plays with light birdshot loads, you'll be at a disadvantage again. The 1187 Police is also designed to be used with heavy defensive loads and may or may not cycle reliably with 7 1/2 birdshot. There is a workaround using a barrel seal activator for the SuperMag but I've never tried it.
For starting out, I would recommend an 1100 or 1187 sportsman if semiauto is your thing. Look for a turkey gun with a 20"-21" barrel change the choke to IC or Mod and your set. Get a choate extension to bring it up to 8+1, it will be close to the length of the 21" barrel. You'll also need an EZ-Loader to help load shells and work the action. Probably the most common setup in 3-gun.
Many shooters are moving from the Remmy platform to the Benelli because of the reliability. If you can tame the recoil the Benelli would be a good option. Others are using Winchester SX2 practicals, suppose to have a faster action than either Benelli or Remmington. Winchester is discontinuing the mark 1 although they are keep the mark 2. FN (who owns Winchester) will be selling the SLP MK1 under the FN name in April. This is my next purchase.
I shoot an HK Fabarm Pump in Heman and typically can outshoot semiautos with limited capacity (down just 1 round)....but if they have the same capacity I have to fight to keep up.