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You don't need to get the Mystery Ticket. Once you've caught 60 Pokemon in your PokeDex, go to Professor Oak and he'll give you the National Dex, then you can travel to the Sevii Islands and catch some Johto Pokemon. If you want the Johto starters, you have to buy Colosseum and trade them from there, or Emerald (complete PokeDex then choose one of them).
Agreed, Colosseum does have all three GSC starters which you can obtain. Also, in the forthcoming Emerald, you can get one of the three starters, but only one (you get to choose which however).