Latios @ Lum Berry
Ability: Levitate
EVs: 4 HP / 252 SpA / 252 Spe
Timid Nature
- Psychic
- Ice Beam
- Thunderbolt
- Calm Mind 
Latios is the lead as well as the main sweeper and it uses Psychic, Ice Beam, Thunderbolt and Calm Mind with a Timid or Modest nature for extra speed or damage and 4 HP, 252 Special Attack and Speed EVs. Psychic is your move with the same type attack bonus and it can hit Poison and Fighting types for super effective damage, Thunderbolt and Ice Beam are your coverage moves and they hit Flying/Water and Flying/Ground/Grass/Dragon for super effective damage too. Finally with Calm Mind you can grab a quick turn one boost to Special attack and Special Defence and then sweep with Psychic/Ice Beam/Thunderbolt. Lum Berry will cure a status problem like paralysis or sleep once, which is useful for making Calm Mind safer to use turn one. As a Dragon and a Psychic type, Latios will have to watch out for powerful Dark, Bug, Ice, Dragon and Ghost attacks as they will hurt it even more.  A lot of Pokémon learn Ice beam for example. The +1 boost to Special Defence from the first Calm Mind use should help with Dark, Ice and Dragon attacks, but you can also use a damage calculator to see how likely Latios is to survive various attacks. You will also occasionally find safe times to freely use Calm Mind as much as you want, however it only needs 6 uses to raise Special Attack and Special Defence to the maximum boost.  Opposing Special Attackers can be good for this but it’s not without risk as a critical hit can bypass your boosted Special Defence. Levitate allows immunity to ground type moves like Earthquake. Suicune or Metagross should be brought in when either Latios faints or they resist something well enough to take few hits.  

Metagross @ Choice Band
Ability: Clear Body
EVs: 252 HP / 236 Atk / 12 Def / 8 Spe
Adamant Nature
- Meteor Mash
- Earthquake
- Explosion
- Shadow Ball
Metagross is the somewhat bulky steel typed physical attacker of the team and it has Meteor Mash, Earthquake, Shadow Ball and Explosion with an Adamant nature and 252 HP, 236 Attack, 12 Defence and 8 Speed EVs. Meteor Mash is unfortunately as good as it gets for steel coverage. The accuracy of the move being the main problem with it, but Hidden Power Steel 70 is also an option if you can rng abuse for it or use Metal Claw if you can’t get Meteor Mash/Hidden Power Steel 70, but it’s really not ideal with the weaker power.  Earthquake and Shadow ball being good coverage moves for opposing Steel/Fire/Poison/Rock/Electric or Ghost/Psychic types and Explosion for when something simply must be destroyed and isn’t a Ghost type or Damp.  The Choice Band locks Metagross into one move until you switch it out and back in, but it makes that one move significantly more powerful. It only works for physical moves though, which Shadow ball is in Generation 3.  As a Steel and Psychic type, Metagross is weak to Fire or Ground attacks and in Generation 6 it gets Dark and Ghost as weaknesses but not in Generations 3, 4, and 5 which is part of why steel is so good for tower in Generations 3 and 4. Clear Body prevents stat reductions like the -1 to Attack from Intimidate Pokémon like Salamence. 

Suicune @ Leftovers
Ability: Pressure
EVs: 252 HP / 252 Def / 6 SpD
Bold Nature
- Surf
- Ice Beam
- Calm Mind
- Rest 
Suicune is the bulky water type and it has Surf, Ice Beam, Calm Mind and Rest with a Bold nature and 252 HP, 252 Defence and 4 Special Attack or Special Defence EVs. Surf hits Ground/Rock/Fire types for super effective damage and is your main sweeping move once setup and Ice Beam hits Flying/Ground/Grass/Dragon for super effective damage as well as not being stopped by abilities like Water Absorb and Storm Drain. Calm Mind to boost Suicune's Special Attack and Special Defence should almost always be what you start with when Suicune is sent out. Rest will put Suicune to sleep for 2 turns as well as curing burn/poison/paralysis and fully restoring HP. Mix in a few Rests while you boost Special Attack and Special Defence with Calm Mind to keep Suicune healthy and then Sweep with Surf and Ice beam.  Leftovers restore a little bit of HP each turn, which is pretty significant for Suicune when it is setup as it can be quite hard to KO with regular attacking moves. As a water type, Suicune is weak to Grass and Electric attacks. Those are both special types in Generation 3, so those Calm Mind boosts make super effective moves less of an issue, but Critical hits can still bypass the boosts. Pressure increases PP usage for moves targeted at Suicune, which makes Suicune excellent for stalling out those moves faster. This Suicune set can be reused in most games with even Brilliant Diamond and Shining Pearl having it as a good option.  Surf is usually dropped for Scald in Generation 5 onwards. Substitute is also an option but you lose another move for it and it’s a one per save tutor move in Generation 3.