Let's unpack this.
First of all, while there if definite continuity in alot of the 'cinematic universes' for Marvel & DC, the movies generally are careful to not make them rely SO HEAVILY on previous movies that you can't enjoy them. This isn't like picking up mid-season of a TV show, or starting in the middle of a book.
Having not seen prior movies or other content you may miss a reference here or there, and you may see a character treated like "Oh hey, you're a pal we already know" rather than being introduced, but the movie SHOULD more or less stand on it's own.
The current plotline of the Marvel Cinematic Universe (MCU) is focussed on the Infinity War, and most of the last several movies have included showing us the component gems that each are powerful, but combined will be unbelievably powerful. But if you just accept that these gems have already been out there, and Thanos has some and is trying to get others, you don't really need to have seen those other movies.
Second, you most DEFINITELY do not need to have read any comics to enjoy the movies or TV shows. They are MORE enjoyable if you have sometimes because they will throw in easter eggs and references for comics nerds like me to notice and recognize. You won't get those in-jokes, but they aren't frequent or essential. They're just little bonusses for us.
Third, in terms of Batman, I wasn't a huge fan of the Dark Knight series of Batman movies. ALOT of people were though. IMHO, the Michael Keaton first Batman is the best Batman movie. The three that follow it are unwatchable garbage that somehow get worse with every movie. You can watch the first of the Christian Bale Batmans in Batman Begins, I think that was decent enough just because it's a sort of origin story, and everyone love Dark Knight because of the Joker, but IMHO it's overrated.
Spider-Man I definitely would watch the first Toby Maguire Spiderman. The second is also good. The third is forbidden. As in DO NOT watch the third one. So bad. I never watched the two 'Amazings" with Andrew Garfield, but everyone I know who has advised me NOT to watch them. And they know I LOVE Spider-man. So for them to tell me not to see it, says alot on how bad they were. Homecoming I was mixed feelings on. But on balance it was good and it ties into the MCU as Marvel/Disney bought the rights back from Sony.
Superman you should watch the first two Christopher Reeves/Richard Donner movies and NOTHING ELSE. I mean, okay, if you REALLY have to, III wasn't THAT bad. It got turned into a vehicle for Richard Pryor which screwed it up, but there were moments that didn't suck. IV is toxic. And avoid the Routh and Cavill Superman movies. They're dreck.
Avengers, both are good. The many, many, many connected movies are mostly okay too. But they vary in goodness. Again, don't worry about the continuity so much, each movie will bring you up to speed on what you REALLY need. The only BAD movies in the MCU run were the first two Thor movies and the Hulk movies. The others, even the weaker ones like Civil War, and Iron Man 2 and 3, are still solid fun action movies.
But watch as many or few as you want. Use Rotten Tomatoes as a guide to which were best. Look at the audience and critic scores of each and watch the ones that have the highest combined score. Critics are wrong sometimes, and sometimes audience scores just reflect how rapidly loyal a fanbase is, but between the two if both are high, usually it's a good movie.
Fourth, Black Panther in particular is, IN MY OPINION, not a very interesting character. This character is one of many that was invented by starting with the premise "Let's make a black character". While I certainly recognize that comics and movies have need of more good black characters, the thing that makes a character good or not good is not whether he's black or white or female or gay...it's being a GOOD character.
Stan Lee didn't sit down and say "let's make a white character" when he made Spiderman. Spiderman was white, but his being white was Lee just writing what he knew...what was familiar to him. What made him interesting was the personality and background and powers and such.
Black Panther is an African Dictator. I'm not sure we should be celebrating dictators. Sure he's a BENEVOLENT dictator running a super-country of sorts, but as a King, he holds absolute power and his people have none. That's a dictator. The character is meant to express pride in black origins, but he's NOT African-American, and he's NOT a particularly good example given that he IS a dictator. He's also NOT particularly interesting OTHER than being King. At least not to ME. IMHO, Luke Cage is 1000% better as a black character showing black pride without descending into the angry black stereotype. You should watch that on Netflix. Unfortunately, that character ALSO is mostly about his blackness.
Fifth, if you're talking movies, Wonder Woman is about the only DC movie worth watching since the Christpher Nolan movies ended. They tried to imitate Marvel and create an extrended movie universe, and it has gone HORRIBLY because they hired a complete hack, Zack Snyder, to be in charge of it. Most of these movies are truly awful. The Marvel movie universe on the other hand has been a hit-machine. Good movie after good movie. I'm probably going to skip Black Panther, but I'll bet even that one will be decent because Disney/Marvel are just in a ZONE that is unmatched. To produce SO MANY movies and have SO FEW of them suck is amazing.
However, on the TV front, IMHO, DC is doing much better. The CW Arrowverse is delightful, especially Flash and Supergirl. Lucifer on Fox is quite good. Preacher isn't as good as the comic, but quite good. iZombie on CW is good. Meanwhile SHIELD, Agent Carter, and Inhumans were all bad shows. The Netflix shows are better, but have been about 50/50. Jessica Jones and Luke Cage were good, Daredevil was okay (the villains were excellent, but DD himself was bland), but Iron Fist and Defenders were awful.
Anyway, that's my $0.02