Your basic strategy is to try to get a wide variety of types and physical/special Pokémon with high base stats. (List of Pokémon by base stats) A variety of types is important so you can counter your foes' types, and a variety of physical and special is kind of important so you can counter your foes' defenses. (Sometimes, but this isn't actually that important, unless you're a really serious player with a list of Pokémon's base stats at hand to know which stat's weaker, and since physical and special are dependent on type in Gen III it's even less so.) High base stats are important because that's basically what determines how strong your Pokémon is.
For example, a bad party would be:
- Sceptile
- Beautifly
- Dustox
- Shiftry
- Masquerain
- Sunflora
A better party would be:
- Sceptile
- Metagross
- Arcanine
- Gyarados
- Jolteon
- Shuckle
You probably don't, however, just want to switch your Pokémon willy-nilly, since trained Pokemon are stronger than Pokemon raised in the wild due to EVs. (List of Pokémon by effort value yield)
If you're just playing rather casually though, pretty much any Pokémon will do and just sticking with one party of Pokémon that you like will be the best strategy, and, tbh, if you're looking to build the perfect, strongest party, you'd finish the plot first and then hatch a new party out from eggs that are specially bred for the perfect moves & IVs and then train them for perfect EVs. You wouldn't try to play through with them originally since you'd have to wait for quite a while in the game to find the strongest Pokémon, and then you wouldn't use those for playing through more of the story, since you can't know what EVs the Pokémon that trainers send out first will give. (Unless you use the "Emerald Berries" that lower EVs, I guess.)
