for a non legendary team i would suggest...
Snorlax - amzing HP, great attack and sp defence, but low on the rest. It will last forever on the field. (unless it gets it with a physicall attack)
Aggron - AMAZING defence. its also a master on attack and will last like a rock on the field while demolishing your opponents.
Weavile - Great speed and attack. can wipe out a load of Pokemon due to its agility and strong attack
Dragonite - just an overall AMAZING Pokemon. Great attacker and lasts a long time on the field. Also can learn fly
Gengar- AMAZING sp attack and speed. Also can learn a combo of hypnosis and dream eater which will probaly feint the opponents Pokemon while gaining HP at the same time.
Tyranitar - Another overall AMAZING Pokemon. Takes ages to feint and in that time it can crush your opponents. (It does lag on speed though)
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The team you choose should have several different types of Pokemon and genders. Try to keep them at a level higher then 50. Dont forget to bring lots of status items.
I would suggest having your whole team above level 50 so you have a chance to beat the Elite Four. I think the Elite Four Pokemon are at level 50-60, so well trained level 50 Pokemon will be good for the elite four.
You keep on fighting Pokemon until you level up.
Level 50's and above Pokemon can be found in cerulean cave.
I would reccomed Viridian Forest and Mt. Silver. In Viridian Forest, the wild Pokemon are level 3-5, but the trainers have Pokemon between level 39-45. Mt. Silver has wild Pokemon from level 38-50.