Well lets consider what the requirements are for a good single run Pokemon
Good offensive stats
Low amount of weaknesses
Good coverage with its moves
Basically, you want an all around, good, average Pokemon. Now lets assume your trading over a Pokemon from another game for your solo run. If so I got just the one.
Kingdra: mystic water/dragon fang
Ability: swift swim (with rain dance) sniper (without)
Rain dance/hydro pump/Draco meteor
Kingdra has a sole weakness: dragon, which it has little trouble handling. With base 95 defenses and base 95 sp atk, kingdra can both take hits and hit back. It's speed is ok as is, but, if you don't mind setting up, you can use swift swim and rain dance to double kingdras speed while also powering up its water type moves. It's STABs alone are only resisted by one Pokemon, empoleon, who you will never see in game. Ice beam nails the grass types that resist water for supereffective damage. The one con about this is that Horsea doesn't evolve into seadra until level 32, at which point you can evolve it into kingdra by trading it holding a dragon scale, so it won't reach it's full potential until you're about halfway done with the gyms, and Horsea is rather weak. You must also give Horsea all the tms and hms before you trade it over.
Here's my other suggestion. This guys available available very early in game, at route 32
Available as mareep early game, decently bulky, and somewhat easy to train. Most of the moves above are learnt by level up, but focus blast and thunderbolt are purchasable TMs. Ampharos is only weak to ground types, the only notable ones being jasmines steelix and pryces piloswine, both of whom can be disposed of with focus blast. It reaches its final evolution at thirty, a decent level, but while its NFE it can still fight decently. It also has good support moves like thunder wave. Also, with its electic stab and power gem, it will bring havoc to lance. However, what makes it a good choice is that well, its a sheep. It's adorable. Plus you can tell your friends you beat the game with a sheep
I know I tend to ramble but thanks for reading. This is just my advice, there are many other viable options for you. Hope this helped.