I wanted to watch the anime, so I was wondering if the anime adapted the light novel closely. Did the anime skip something or made changes to the plot?
You can watch the anime without first reading the LN, but there is a lot more stuff after the anime ends. There's not much difference during the anime other than slight changes and some of the jokes in the anime are improvised by the voice actors. The LN and manga go further about the lore and characters more though.
I am currently doing both, having watched both series of the anime only last week, and now reading the LNs.
The LNs have more information in them, but the anime is definitely funnier, as the physical jokes and expressions gain from the visual aspect, and you get a VA performance that gets across the tone of the dialogue (there's a lot of scenes of characters crying out in comic distress that come across much funnier seen than read).
As for a close adaptation, the benefits of it being a LN are that the character design is straight off the picture pages of the LN; and the dialogue was between close and exact from what was in the LN.
You will miss out on some extraneous detail - a certain recurring character has their introduction done in a flashback as opposed to the full chapter it gets in the story - for example, but very little from the first LNs that the two series are based off was missed.
In my opinion, I'd go with the anime first. It won't take long to do, and you'll get the full impact of the visual jokes that you'd know were coming due to having read the LN. If you then go back and read the LNs, you'll receive a little more backstory on certain characters, but you won't have missed out on anything important.