ThatCrazyAlexGuy, Pokemon Blue and Yellow are easy enough as they are. You don't all the starters and the Uber (Ultimate and Powerful) pokemon unless you're going to battle different people. In your case, that doesn't sound like it will happen, you having Blue and Yellow and all so here goes a list which I'm not sure about. I haven't played Red since like, 2002 so I'm not sure about movesets. Someone else might be able to help out there but back when I played most of my friends ran these pokemon in a team.
Scyther:Not powerful and not an OU or an NU but fast. I'd choose it as my team leader.
Chancey:Good against Special Attackers.
Venusaur:Strong Pokemon, OU these days in LG and FR.
Flareon:Strong Special Attack, fast and can be more versatile than Vaporeon. Not sure about Jolteon.
Rhydon:Good at DEf against Physical Attackers.
Gyarados:Could just about own anything with good Attack and an EQ(Earthquake).
I'm sure that some guys on this forum could make much better pokemon parties but those are the pokemon that come to mind.