You can make it through the storyline with any starter just fine, but I personally just do not like the Tepig line. One because I'm pretty sure Nintendo just wanted to make us mad with another Fire/Fighting. Two because Its better moves are only learned later on, Tepig and Pignite kind of aren't good at all, and even Emboar can be taken down with ease, though admittedly I love his design.
Oshawott line is good, Samurott can do well in most situation.
I prefer the Snivy line. They learn moves fast, they ARE fast, and I mean just LOOK at them! They just KNOW they're gonna beat you down! But yeah, Serperior is the fastest starter, has solid defense, has a good variety of attacks, and can set itself in several different roles, whether it's offense, defense, stalling, annoying, and the like.
Using every starter to run through the game <<