Skip episodes 1 and 2.
Watch 3 through 10 to be introduced to the main 4 characters.
Episodes 11 through 24 introduce several of the recurring supporting characters. Episode 15 is funny because it's a competition between pets. I liked 17 especially because it introduced the series's main villain. 18 and 20 were hilarious for the random shenanigans whenever Gintoki and the Shinsengumi police team up.
And this is where I started to skip around. >.<
Episodes 31 and 32 have Gintoki experience amnesia and the gang tries really hard to help him regain his memory. <3
Episode 40 through 43 introduce Kagura's daddy and her backstory. <3
Episode 45 describes Sadaharu's backstory. <3
Episodes 58 through 61 are epic and badass, though I prefer the first Gintama movie's adaptation of this arc for its superior quality. :3
Yeahh, I kinda jumped around a bit. I definitely love the humour in it though. Watched an episode where a sad story was being told on the radio, and it turned out to have a completely twisted ending. Gin's reaction to it was hilarious ;D
Yeahh, it's kind of a cliché. I can only think of a few where the main protagonist has both parents D: