Persian is often better used late-game, as it won't be paralyzing many Pokemon like Tauros would. After most of their team is disabled, Persian is wonderful at cleaning up the mess. Being faster than Tauros and as fast as Starmie is nice, as most of the time the opponent will not let these Pokémon get paralyzed. Try to keep Persian free of paralysis too, as it loses most of its usefulness when it is paralyzed.
Slash is the main attack you will be using. Hyper Beam is for when you need something a tad stronger or are trying to get a critical hit using Persian's Speed. BubbleBeam is to deal with Rhydon and Golem. Thunderbolt can paralyze Gengar on the switch and hurt Cloyster. Body Slam is useful to deal damage with STAB and give a chance at paralysis. You probably won't be using the last move too much anyway, so you don't need to feel hugely pressured with the choice. Screech can be of use, especially against Starmie, which is OHKOed (most of the time) by a Hyper Beam after a Screech, so they either must switch or risk dying. If you are left one-on-one at the end of the game, Screech will win you the game.
Screech can help Persian defeat Starmie and Chansey that aren't paralyzed. Against Starmie, however, the secret is to Screech and then BubbleBeam. BubbleBeam would bring Starmie into guaranteed KO range for Hyper Beam, and also has the chance of catching your opponent switching Rhydon or Golem into Persian who aren't aware of this strategy and are expecting Hyper Beam.
None of the options that haven't already been listed are particularly useful. Don't bother with Thunder as it won't 2HKO Starmie or OHKO Gyarados. You can use Mimic, but Persian is probably better at using its own moves than anything else Mimic could get.
Checks and Counters
Gengar stops it completely, as the best Persian can hit it with is a weak BubbleBeam or Thunderbolt, even though the paralysis chance from the Electric move should be noted. Snorlax is also a good counter as it can take 3 critical hit Slashes thanks to its massive HP while delivering hard-hitting Body Slams. If you can paralyze Persian, it's pretty much dead. Tauros, Exeggutor, Alakazam, and the legendary birds can take it one-on-one due to their Speed or powerful STAB attacks.