I recently started playing through Poke'mon Blue again after finding my old Gameboy, I needed something to distract me from my studies. Though, I don't want to go through the game using the same Poke'mon as I did as a child, so I'm trying to put together a team of Poke'mon that are not generally used. At the moment, I have
Farfetch'd is definitely a rarely-used Pokemon. Go the whole game without evolving your Wartortle, that would be a cool rarely used pokemon.
A bunch of friends and I are doing a scrambled eggs game in Black and White 2. Everybody's breeding pokemon and we're trading the eggs at random, whatever team you end up with will be the team you use in game. The idea is to fill the game with pokemon that are cool but you wouldn't normally use, lower tier pokemon, pokemon that you would normally find really late game and wouldn't be able to actually use for the story line (of course, I use the term "story line" lightly). We're all getting our pokemon bred now. It should be a very cool game, kind of chasing after a similar experience that you are right now.
Always good to see someone take up the incentive to play through ingame again - never mind the ones who are making light of you simply wanting to do things your own way.
Once you've finished that run-through, if you find yourself wanting to do another run, then there's a wide selection of "challenges" that you can impose on yourself for subsequent runs. Feel free to ask for suggestions (or even do a websearch) if that time comes.
Where logic won't work - I will PAL Gamers unite - http://www.gamefaqs.com/boards/277-pal-gaming