Well me and a buddy were talking about this earlier today, about what we would want to see in a mature Pokemon.  After a bit of talk, we came up with what we want the beginning to be like and some other nonsense.
Note: Most of what we thought of is fairly nonsense and may offend those who hold Bidoof close to their hearts.
 
Right.  You start the game naked except for a belt with a single pokeball containing a Squirtle, lying at the side of a route with no memory of how you got there.  From there the first little quest (we imagine it be far more "RPG" than the normal Pokemon games) which is to get yourself a sweet cloak.  To do this you have to find a Bidoof waddling about in the grass and get Squirtle to beat the guy down until it is dazed, then you leap into the fray with your trusty skinning knife (that Squirtle gave you as a gift) and cut the poor beast in such a way as to not damage the silky, silky fur.  Commence skinning mini-game (stylus controls coming into play perhaps?).
 
Boom.  Sweet cloak to protect your pink (or any other hew you care to play as) flesh.  Now you have a choice:  continue along the route or improve that sweet cloak into a even sweeter cloak by finding a pidgey, plucking it and attaching the feather to give yourself a nice feather collar.  Anyway continuing on you come across a Charmander and here is the fabled "MORAL CHOICE" system.  Since you can only have one companion at a time and you don't have access to a PC yet, you have to decide what to do: leave Charmander alone and run away (this lowers Squirtle's opinion of you), jack Charmander and turn his hide into some fire-proof chaps or jacking Squirtle - who helped you out, giving you a skinning knive and helping get you a sweet cloak - and splitting his shell to make some rudimentary pauldrons.
 
The game continues like this, your party expanding slowly into the traditional six slots and jacking Pokemon for loot (bag yourself a couple of Rattata and you've got some nice gloves) until you recover your lost memories and discover the secret behind how you ended up naked on that route with Squirtle.