Am I supposed to have multiple high level pokemon?
It's disadvantageous to stick to a single Pokémon, but not all that impractical. There was once a run of Pokémon Yellow, I believe, done with just a Pidgey.
You don't need multiple high level Pokémon, it simply helps. Type coverage is the main reason - for example if your highest level Pokémon is just a Fire type and can only do Normal and Fire attacks, then you stand a hefty disadvantage against Rock types who resist all your attacks and can deal double damage. As well, Fire and Dragon types will block you completely, while Water types mostly block you and also do double damage.
Having your other Pokémon be of equal or near level as your highest helps in survivability of that other Pokémon as well. For example, a Ground type with high defense like Sandslash can help protect against the Rock types while also taking them down. This also gives you the opening to fully heal your primary Pokémon in between the assault of your opponents - it's a lot easier to keep your primary Pokémon in top shape when your supporting ones don't fall down in a single hit. At this stage, though, it probably helps to make those "assist Pokémon" simply capable of taking down foes on their own right.
It's ultimately up to the preference of the player, though. It's fairly common for people to stick solely with their starter of choice, and by sheer force of their levels take out all opposition. As long as you have good type coverage with it (for example, Charizard can use the TM to learn Earthquake to help mitigate some of the problem foes), enough of a level advantage will keep you on top.
For single player, what you are doing works. It's a game designed with children playing in mind, so pretty much anything works for the story.
As far as enjoyment goes, the battles are much more fun if you have a team of 6, because if you don't battles end up like so near the end:
Lvl 85 Charizard vs Lvl 55 Elite Four Pokemon
Is the pokemon resistant to fire?
- Yes - Use Cut.
- No - Use Flamethrower
If you want to play multiplayer (unlikely since it's Pokemon Blue), your level advantage goes out the window so you need multiple levelled up Pokemon. The grinding does go through the roof though, which may be more of a detriment than caused by the above.
In general, my technique with the campaign is to scale up the number of Pokemon I use. As you've mentioned, the Pokemon available to you at the moment are not too appealing * . Obviously, you won't make a team of six from them, and there's no point grinding levels on them.
It varies a bit game by game, and obviously which Pokemon are available does impact it, but my general technique is to have:
- 2 pokemon by the second gym
- 3 by the 4th
- 4 by the 6th
- 5 + HM Slave or 6 Pokemon by the eighth gym
This reduces the pain by of grinding because you're not trying to raise too many at once.
The other thing to reduce grinding with a full team is to accept that Pokemon levels are going to differ somewhat. No, you are not going to be able to level up your water pokemon that much in the power plant, for example. I often have as much as a 10 level gap between my highest and lowest Pokemon, even when I have a full team.
*: One thing I will mention is that even though the choice is poor at this stage, it's not as bad as it looks. Here are some Pokemon you may have missed
- Pikachu (5% encounter chance in Viridian Forest) - Very useful against Misty.
- Nidoran (40% chance to encounter in route 22, to the west of Viridian) - Poison type, not as useful as Pikachu but it's final form is quite good. In Blue, you will mostly encounter the female variant, which evolves into Nidoqueen.
You can definitely play the way you're doing it, but I personally prefer to keep a team of relatively equal level so I can counter nearly every Pokemon I come across. I've always played this way; I'm too scared of blacking out. I like my money! ;)
As you've recognized, if your Charmander blacks out you're in trouble :P If you continue through the game the way you are playing you might encounter some difficulties (namely, Misty), as already pointed out in wonderful detail. Also consider that you will have to battle your rival on multiple occasions, and he will always have the hard counter to your Charmander. On top of a Kadabra, soon enough. Ugh.
Another thing to worry about is the level restriction. If you fight with primarily one Pokemon, it is going to gain a lot of experience through the many trainers you cannot avoid or accidentally walk in front of. But if it gets too high-levelled, it will not obey you until you have the proper badges. And then you're REALLY screwed :P You're capped at level 30 until you beat Erika, who is quite a ways away, so be careful :) After Erika you're pretty much okay on the level problem; you get enough room that you probably won't hit the cap.
Good luck!
Oh, another thing. A lot of early Pokemon aren't great, it is true, but I highly, highly, highly recommend catching an Abra and levelling it up (you have to send it out first and then switch immediately to another Pokemon since Abra can't actually attack--don't worry, Abra doesn't need many exp points to level and evolves at 16) to evolve into Kadabra. Kadabra is an amazing Pokemon to have. Weak in defence, but with incredibly powerful attacks and fast enough to hit first.
Because its evolved form is so good, Abra are hard to catch--their only move is Teleport, so as soon as you find one it just Teleports away. I usually level up a Pikachu along the way (I need Pikachu anyway for Flash in Rock Tunnel) until it's fast enough to Thunderwave an Abra before it can Teleport away. Then I pray it remains fully paralyzed so I can toss out a Poke Ball. It can take what feels like forever because often they manage to Teleport regardless, but it is worth it. A better way to catch an Abra is to put it to sleep, but it's a lot more annoying to level up a Jigglypuff or a Butterfree. Pikachu level up easily because they are super effective against the Zubat in Mt. Moon and the Pidgey which are ... well, everywhere. Pikachu are also quicker than the other options, which is good since Abra are pretty fast.
You can first find Abra in the grass if you travel the Nugget Bridge north of Cerulean City and then go left a little, the long patch of grass below has a 15% chance of yielding Abra. If I pick one a lv 10 one then and switch it in and out while fighting the trainers on the way to Bill's house, it without fail evolves by the time I've gotten through them :D
Also! (I talk too much, I know.) People tend to think Rattata is a bad Pokemon because it is so weak. However, it's fast enough that you can level easily against early trainers and in Viridian Forest and it learns Hyper Fang at lv 14 which is a super good attack - especially because it learns it so soon. It'll take out Pokemon around its level easily with Hyper Fang. And when Rattata evolves (lv 20, so it'll be doing that early; mine always evolves somewhere in Mt. Moon or soon after) its attack and defence jumps quite a bit higher. Suddenly it's not so weak ;) My Raticate is actually my strongest Pokemon, going by stats, even stronger than my starter Squirtle/Wartortle (though unfortunately my Squirtle happens to be a less powerful one this time around); and it's second highest to Wartortle in defence. And because Raticate's type is Normal, it doesn't have a weakness. It can't attack Ghost Pokemon, of course, and it does very little against the Ground and Fighting types, but the awesome thing is you can teach it an attack that will help it counter those types with ease. (I like teaching it Dig, and later sometimes Ice Beam if I don't feel like giving that to Blastoise.)
Okay, now I'm done. Sorry, I love Raticate. I keep it with me the entire game, and use it to help take down the Elite Four. I end up with my starter, a couple of Legendary birds (one with Fly), a Kadabra, another Pokemon which varies (sometimes a super low-level Grass Pokemon so I can cut all the stupid bushes--I don't like fighting with Grass Pokemon so I just give one Cut but never use it), and then Raticate. It's such an underrated Pokemon.