Can anyone suggest a Pokemon that I should carry around with me. I carry..

Well, as much as I hate how Mr. Mime looks, I would definitly recommend him here. Give him the following:
Nature: Timid (You'll be wanting speed, no need for attack)
Hold: Leftovers (Last just the bit longer)

Then give him the following move set:
Calm Mind
Barrier
Baton Pass
Psychic

First of all, send him out and PUT UP SOME BARRIERS because his defense is pretty bad. And then sit around and Calm Mind a few times. Because of your added defense and already amazing special defense, you'll last quite a few hits. And then obviously Baton Pass to one of your many special sweepers. I recommend him because most of your Pokemon can use awesome special attacks and the added defense, specials attack and defense would totally own, especially to Espeon, or even Sceptile (increased defense + already awesome speed + special stats to match Mewtwo = wow, time to take on 6 Rayquazas!) Use Psychic if he's a bit screwed, as in cornered, you'll still have the special stat gain from Calm Mind and also STAB (Same Type Attack Boost).

Unfortunately, you'll be having a very hard time trying to catch a Mr. Mime in Leaf Green, or any other advance pokemon games, but not to worry! Catch yourself an Abra, and then either go through the Diglet's Cave from Vermilion or Cut in from Viridian path place thing, and there is a house, and inside a guy will want to trade a Mr. Mime named Mimiem or something for your Abra. Well, you get added experience points in exchange for a stupid nickname...
If you can find another pokemon that can learn Calm Mind, Baton Pass, and a defense booster e.g. Barrier, Iron Defense, Acid Armour...hey, actually, if Vaporeon can learn Calm Mind, USE HIM INSTEAD! Do whatever I told you to do for Mr. Mime to Vaporeon, but use Acid Armour instead of Barrier, and either Surf or Hydro Pump instead of Psychic.

Well, aren't you a lucky guy? Guess which version you can only catch Electabuzz? (Happens to be Fire Red...)

And also, if you don't mind, you could post up the move sets for your other pokemon.

Oh yeh, I wanted to know, can Steelix learn Bulk Up? Sorry, I just thought it would be a waste to post a simple question.

1.how about Umberon,he is cool and is also a very helpful pokemon.

2.The power plant is where you catch Electabuzz.

This is for en_ryu

Dragonite (Scales) lv.76
Leftovers
Thunder
Flamethrower
Outrage
Fly

Blaziken (Blaza) lv.82
Charcoal
Fire Blast
Blaze Kick
Sky Uppercut
Substitute

Espeon (Fritzy) lv.65 ( In training only got 3 days ago)
Twisted Spoon
Psychic
Psybeam
Calm Mind
Morning Sun

Sceptile (Screp) lv.83
Miracle seed
Solar Beam
Dragon Claw
Leaf Blade
Aerial Ace

Swampert (Smirty) lv.81
Mystic Water
Earthquake
Surf
Ice Beam
Dig

Im not really sure if Steelix can learn Bulk Up, I havnt got one from my Leaf Green yet.
Thanks for your help about the Mr. Mime to. Cya

If anyone reads this including en_ryu can you please post back what you think of my team.

Nice move sets , however:

Dragonite, I would recommend exploiting his attack stats:
Earthquake
Aerial Ace (Fly wastes a turn)
Return/Thunder Wave
Brick Break/Rock Tomb

Thunder Wave quick enemies and just sweep their team. Well, if you're crazy on killing, instead of Mr. Mime, you can add in Ninjask. Swords Dance, Baton Pass, two other physical moves. Swords dance, his added Speed boost thing, baton pass to Dragonite, works like a physical Mr Mime.
If you must have a special attack, give Dragonite Ice Beam, or Dragon Claw, replace Brick Break.

Blaziken: If you must have substitute, go for Focus punch instead of sky uppercut. Sub, then F.Punch, you won't be flinched. If not, keep Sky uppercut, replace Sub with Swords Dance (learned from move tutor in leaf green, 7 Island bridge.) Not sure if he can learn swords dance, but worth a try. Then replace Blaze Kick with Earthquake or Return and replace Fire Blast with Overheat. Blaziken's attack is better than his special attack. Swords dance, if you can learn it, if not, Bulk Up, sweep the opposition with sky uppercut and earthquake, get speed from Ninjask if you want, and Overheat if something crazy comes along. ;) You'll fare well.

Espeon: Wow, where did you get Twistedspoon?
Try playing around with Espeon's hidden power, if it is Fire or Dark, Lucky! Use that instead of psybeam. If not, replace psybeam with Shadow Ball. Well, espeon has a simple tactic I'm sure you already know: C. Mind, M. Sun, C. Mind, sweep (and BTW, sweep means to use your powerful attacking moves, I'm sure you've already know though). Sceptile: Cool, however don't use Solar Beam without Sunny Day, Sceptile's defenses are quite bad. Use...not sure actually, any special attack, you can play around with hidden power again if you haven't used it on Espeon.

Swampert: All is very good, except dig. It's useless, unless you happen to keep running into caves without Flash and can't get out. I don't know why but Swampert, like Feraligatr, has more attack than special attack...? Anyway, replace dig with whatever you want, preferably physical. I recommend Brick Break or Toxic.

Use Ninjask, unless you have a real dislike for R/S/E pokemon. If you know anything about EVs (Effort Values) pile all of them into Ninjask's defense and HP, i.e. When you first catch a Nincada, give him a Macho Brace and kill about 200 Clampearl (no joke) and 50 Whismer. Or 150 Clampearl and 100 Whismer, up to you. I'm sure you can set up an intelligent way to count, instead of tallying each one you kill, you'll be there counting more than battling. And...use Mr. Mime if you prefer special attacks.

Of course, all of my rant is optional, might get a bit complicated, but I hope it helps...