Cartoon always seem harder to me - I prefer to actually see the person who is speaking. 

When I'm watching something in Spanish I like to listen and have the subtitles on as well. That way, if I miss something spoken, I can glance at the subtitles to catch up. Sorry, but I don't have any specific recommendations based on your language level.

Maybe try a bit of intensive listening? For example: pick an episode, watch it first in English without subtitles, then watch it with subtitles to check your understanding and then again, do a bit of "shadowing" (meaning you repeat a portion of native-speaker dialogue almost simultaneously with hearing it).

You should definitely watch something that you are interested in/enjoy, possibly a series that you have already watched dubbed in Italian. It is scientifically proven that our brains retain information easier if there is an emotional connection to be found.

Don't worry if you catch everthing from the very begining, you can always go back and watch again (without/with subtitles). And again. :-)

All the shows Jmat listed above are really good. 

Here are some more for you to choose. These are the ones that I'm currently watching/re-watching:  Modern Family, Parks & Recreation, Two and A Half Men, The Mindy Project, The IT Crowd (UK), Brooklyn Nine-nine, Graceland, and You're the Worst.

I just looked up Peppa Pig and it looks like it's aimed at very young children. Maybe you should try looking for something aimed at children a little bit older. Here are a few shows I used to watch: Spongebob Squarepants, Jackie Chan Adventures, Futurama, Dragonball (and its more serious sequel, Dragonball Z), Yugioh, Pokemon etc.

If those are too easy, you should try something aimed at young adults. Here are a few random ones I can think of: Dexter, Sherlock, The Big Bang Theory, Supernatural and How I Met Your Mother.