In-game, between all of these, I would pick Poliwrath.
First, Politoed is useless without Drizzle, as it has not got any very high stat. It has its use in OU because of Drizzle, and competitively, Rain Teams has 99.999999999999999999 % of the time got this guy for setting Rain automatically. It has a fairly good movepool, but is not recommended in-game. Over Wi-Fi and Simulators, it should be fine.
Then, Vaporeon, like Politoed, is not useful in-game. It has excellent support move, stuff and stuff, but all of this, like for Politoed, see a use over Wi-Fi and Simulators. In-Game is very offensive, so you will often put 4 attacks on your Pokémons. Over Wi-Fi and Simulators, however, you feel the real game of Pokémon:Strategies, Predict, Risk and Reward and more. You are battling a human with a mind, who thinks before acting. Robots in the game are easy to battle. A super effective move, and then look at them fainting.
Lapras has a good support movepool again, in Perish Song, Ice Shard and Roar for phazing. So like the two formers, it has not got a good use in-game. You can make it a slave, too, but if you can, Dragonite and Samurott are the best slaves. Bibarel is also a funny slave to use, but the two formers learn every HM moves (okay, Samurott definitively has wings XD). Well, Lapras is better use at NU.
Poliwrath can run a full attacking moveset, and in-game, it is perfect:
- Brick Break
- Rock Tomb
However, competitively, it is ALL different.
Lapras is okay over Wi-Fi. It gets setup moves like Curse and Dragon Dance, has STAB Ice Beam, but a crippling weakness to Rocks. Definitively not your choice. Lapras
If Poliwrath is good in-game, competitively, it is a bit different. Poliwrath functions as a wall, but Tangrowth is easily a counter to every of its sets. Poliwrath won't be your competitive choice. Poliwrath
Toad's got well rounded stats and Drizzle. It is to include in a Rain Team. Otherwise, forget it.
Your choice. Vaporeon's bulky, and supports very well your competitive team with access to Baton Pass, Substitute, Acid Armor, Wish, Heal Bell and Scald. Vaporeon fulfill the role of a bulky Water Pokémon, and has monstrous HP. Vaporeon
I hope this helps.
~ Sincerely yours, Blitz of Justice.