My suggestion.

Okay, you do the starting stuff with naming yourself and wake up in your bed. You go downstairs and you father is there (Because mothers are overrated). He tells you that Professor Pine was looking for you. You walk out of the house and Gary (Or whatever you named him) runs over to you. He tells you that he got a starter Pokémon and that he is going south to start on his journey (Not sure if we make him nice or a jerk yet). You go to Professor Pine's lab and she gives you the choice of the three regional starter Pokémon - Grimer, Wailmer and Shuppet. You head south and arrive at Route 701.

Route 701 is a grassy route. You can find a Potion, Antidote and another Potion.
Wild Pokémon:
Seedot - 10%
Growlithe - 10%
Sentret - 20%
Pidgey - 20%
Vulpix - 10%
Lotad - 10%
Zigzagoon - 20%

There is also a pond.
Surfing:
Psyduck - 40%
Azurill - 20%
Marill - 5%
Slowpoke - 25%

Old Rod:
Magikarp - 20%
Remoraid - 30%
Feebas - 1% (We'll change its evolution to Water Stone)
Poliwag - 30%
Goldeen - 19%

Good Rod:
Staryu - 20%
Shellder - 40%
Carvanha - 20%

Super Rod
Gyarados - 60%
Seaking - 25%
Poliwhirl - 20%
Relicanth - 5%

You continue south and arrive at the next town.

Next Town:
There is a Pokécenter, a Pokémart, a Gym and a house where a man will give you the Old Rod.

When you arrive, you'll encounter Gary, who will tell you that the gym is currently closed, so he's going to go back and ask the Professor. You can garb the Old Rod, but you need to go to the Pokémart. The assistant will ask you to deliver a parcel to the Professor. Another assistant will sell Potions and all five status healers. You then head back to the first town. At the gate, you encounter Gary, who will battle you.

Gary Battle 1:
300 Pokédollars
Yours -> His
Grimer -> Wailmer
Wailmer- > Shuppet
Shuppet -> Grimer
It's at level 6.

He runs off to the lab and you follow him, because you have a parcel to deliver. You give it to Prof. Pine and she says that it was a delivery of "Trainer Kits." Since she forgot to give them to you and Gary before, you get it now.

New Trainer Kit:
Pokédex,
Running Shoes,
Itemfinder,
3 Potions,
2 Antidotes,
2 Awakenings,
2 Parlyz Heals,
2 Burn Heals,
2 Ice Heals,
5 Repels,
5 Pokéballs,
1 TM 43 (Or whatever Secret Power is).

She then tells you that the gym is closed because suspicious people were seen in Icicle Cavern, to the east of "The Next City."

You head back and go east, bringing you to...

Route 702:
Wild Pokémon:
Geodude - 30%
Nosepass - 5%
Taillow - 20%
Swinub - 20%
Clefairy - 5%
Nidoran - 10% each.

Edit: This is a rocky route with patches of snow.

You can now buy Pokéballs, btw. On this route you can find two Stardust hidden in boulders. Right in front of you is the entrance to...

Icicle Cavern
You can only access Floor 1 at the moment, so I'll only cover Floor 1. There is no Water on Floor 1.

Wild Pokémon:
Spheal - 30%
Snorunt - 20%
Zubat - 10% (Keep Zubat levels down throughout the game.)
Seel - 20%
Geodude - 20%

Here you will encounter Team Rocket/Team We might change them.

First Grunt:
50 Pokédollars
Poochyena level 4
Rattata level 4

Second Grunt:
50 Pokédollars
Houndour level 5

Third Grunt:
50 Pokédollars
Spinarak level 3
Weedle level 5
Venonat level 7

Final Grunt:
250 Pokédollars
Zubat level 3
Rattata level 3
Absol level 5

After you beat them, you find an injured Lapras. The storyline has you find a Master Ball and catch the Lapras (Cutscene), then teleports you back to Professor Pine's lab. She takes the Lapras into care and you leave. You can then take on the gym. It's a Dragon Gym, but that's it for my suggestion.

Not bad, but Icicle Cavern and the Gary Battle looks a little difficult.

And Ice type don't deserve to be at the beginning, anyways. They're too powerful.

And I sorta don't agree with Lapras being at the beginning, anyways.

The Lapras isn't usable, it's part of the storyline. And Ice types aren't too powerful. I'm having it be a change from what it normally is and letting people get Ice types early.