Guess the closest comparison of this show would be to combine
Rurouni Kenshin [Samurai action in earlier time periods with many characters based on Japanese historical figures/folklore] with
Space Dandy [Sci-Fi Space Comedy that has aliens]. Comedy style is similar to
Daily lives of Highschool Boys.
Basic series synopsis
The story focuses on an eccentric samurai, Gintoki Sakata, his (partial) apprentice Shinpachi Shimura, and a teenage alien girl who's from one of the strongest races in existence: Kagura. All three are "free-lancers" search for work in order to pay the monthly rent, which usually goes unpaid anyway. The story takes place in the Edo Period, but instead of the Europeans invading in the late 1860s they are invaded by aliens, which they call Amanto.
First off Gintama anime is like at 270+ episodes [plus two movies and two/three OVAs] and counting so if your gonna give it a try your gonna have a serious marathon ahead of you so don't burn yourself out. Even though most of the episodes are self contained sitcom style that may give the impression that there is no advancing plot, but it actually does have a continuation and watching the episodes out of order can confuse you.
Also have to keep in mind the first two episodes are actually filler [come back to it much later if you want] that will confuse you [they assume your pretty ahead in the manga when those two episodes aired] and is advised to skip straight to episode three which is the real series pilot. Even then fans pretty much agree that the early part of the anime [first 20~ or so episodes] is the weakest in terms of comedy/action delivery because it focuses on character introductions/setting building since that plays a bigger role later.
About the five reasons in no particular order. Links are scene excerpts and not really spoiler]
1.
The Comedy. Some of the humor will fly over your head because it may be
too Japan Cultured, but a lot of it is still western friendly enough especially if your at least a casual anime fan since references [some
more blatant then others] will start flying. The comedy isn't just the references either because it has a balance of
toilet humor,
overemotional reactions,
genius trolling moments, regular
fourth wall breaking to rival Deadpool, and more subtle
wordplay comedy. Tsukkomi reactions [playing the "straight man" when someone is being silly] is also a regular sight. If your not a fan of Gintama humor then you may find yourself struggling with this series since the comedy is the large piece of the pie.
2.
The Action. I'm not gonna lie the action in this series doesn't appear nearly as often as compared to the comedy, but when it actually does appear it makes you forget that the previous episode was just pure comedy since it actually looks like a
violent shonen action show. The series usually has 'serious arcs' making semi regular appearances after a certain amount of comedy episodes. You have to keep in mind while the cast may be fucking around a a lot, they are capable fighters especially since several of them had connections to the Samurai vs Amanto war that happened prior to the series beginning. It's not just the action either because there are some legitimate sad moments [if I link any of those then it's pretty hard to dodge spoilers] that are sprinkled around too when shit hits the fan. Funny enough even during 'serious arcs' the characters still would regularly have a sense of humor depending on the scenes and still try to make you laugh since it can switch between comedy and action effortlessly.
3.
The Characters. The above two reasons would not work at all without the characters in question. They range from the main cast of the
Odd Jobs Trio,
the Shinsengumi police force, and even a
Madao. They all have great chemistry with each other whether for comedy or action. The VA talent for the characters also enhances the experience with the likes of Sugita Tomokazu, Rie Kugimiya, Kazuya Nakai, etc.
4.
The Music. The OST is great since it is large and ranges from
laziness,
weirdness,
emptiness,
sadness,
craziness,
danger, etc. The various OP and ED themes are great too with
this and
this being my personal favs.
5.
Easter Eggs
They literally fuck around a lot with hidden easter eggs in the anime like joke OPs, endings, previews, etc that really spices up the episodes kind of like what the couch gags in the Simpsons did.