Playing through yellow for the first time and I have what I can imagine is a very generic team at the moment of Pikachu, Ivysaur, Charmeleon, Kadabra, Butterfree & Squirtle who i've just got after beating the third gym. The issue i'm having is deciding what to do with my HM's. I've just seen I can't unlearn them in this game so don't want to teach it to someone and then regret it later. Half tempted to give it to Ivysaur and put up with it or just keep someone else in the party to be a HM slave like Mew or something like that.
As far as HM's go you can give Squirtle surf as it is the best water attack in the game (hydro pump is more powerful but it miss easily). For gooseberry fool like Flash and Cut find a Pokemon who can learn those moves so you don't have to ruin your main Pokemon. Strength is good on your main Pokemon if they have high physical attack, unless those Pokemon can learn slash in which case never give them strength. Fly is alright in your mains if you are just using it for single player, it's convenient to have on you at all times and it lets you dodge attacks by the AI, against other players though it's pretty gooseberry fool.