I think for something different, you pick your Pokemon when you start the game when you name yourself.
Then when you wake up the Pokemon you have chosen is sitting at he foot of your bed and starts following you (similar to HGSS).
Then on your mum's advice you visit the regional professor who is in the next town and she said that Pokemon had escaped from the lab and was meant to be a choice for a new trainer but it has bonded with you so she lets you keep it and gives you its Pokeball and a Pokedex.
Then enter the rival, who chooses the type better than yours and says this is the one i wanted anyway and decides to battle you which forms a strong rivalry.
I think that would be at least a nice twist on getting your Pokemon.
Then when you wake up the Pokemon you have chosen is sitting at he foot of your bed and starts following you (similar to HGSS).
Then on your mum's advice you visit the regional professor who is in the next town and she said that Pokemon had escaped from the lab and was meant to be a choice for a new trainer but it has bonded with you so she lets you keep it and gives you its Pokeball and a Pokedex.
Then enter the rival, who chooses the type better than yours and says this is the one i wanted anyway and decides to battle you which forms a strong rivalry.
I think that would be at least a nice twist on getting your Pokemon.