The early game of Pokémon Colosseum is about establishing a solid foundation for your team and understanding the core mechanics. Your starter Pokémon, Eevee, is a versatile choice, and its evolutions can be obtained later. Focus on snagging Pokémon that provide good type coverage. Early on, you'll encounter various Cipher Peons and trainers. Prioritize snagging Pokémon that can help you overcome the immediate challenges, such as a Pokémon with Electric-type attacks to deal with Water-types, or a strong physical attacker.
As you progress through Phenac City and the surrounding areas, you'll be introduced to the concept of Shadow Pokémon and the purification system. Make it a priority to purify your snagged Pokémon as soon as possible. This not only unlocks their full potential but also makes them more reliable in battle. Don't be afraid to retreat and heal if a battle is proving too difficult. Building a balanced team of four to six Pokémon that can cover each other's weaknesses is a key strategy for long-term success.