Vikings: The North Atlantic Saga (2000) is well researched, lavishly illustrated, and cheap. I think it's one of the best introductions available, although Sweden and the Baltic are generally outside its scope.

Vikings: Life and Legend (2014) is perhaps the most popular introduction right now. Again, it's replete with lavish illustrations, although I'm not a fan of its elite-warrior-male focus, which risks leaving other elements of society out of the picture altogether. It does do a better job of bringing in eastern Scandinavia.

The Oxford Illustrated History of the Vikings (2001) suffers from some of the same problems as the above two, focused primarily on the activities of male elites in the west. It's not quite as eye-catching as the others, but its rapid political narratives organized by region are perhaps the easiest way to get a general understanding about what was going on, depending upon what kind of history you're used to reading.

The Viking World (2008) is a more scholarly introduction. It's full of short chapters written by experts with very few images. If your interests take a more academic turn, such as What did viking towns look like?, then this is your best resource, especially if you dig into the bibliographies at the end of each chapter.

The Vikings (1987) is a very old read. It misses a lot of new research and a lot of new questions. It is, however, a traditional standard, and unlike the above volumes, it's pocket-sized and good for travel. So it remains great for an introduction, as long as you read it with a critical eye and use it to raise questions rather than to provide conclusions.

For primary sources, there's any number of good options. The big collections of saga books look impressive, but they're often easy to read in short bites. Longer, more important sagas, such as Njal's Saga, Egil's Saga, or the Volsunga Saga, are generally sold as individual volumes. I generally recommend Penguin editions, which are cheap, readable, and have good introductions. Avoid the freely accessible sagas online, which were translated in the 1890s and could deaden the enthusiasm of even the most stout-hearted reader. There's also poetry collections known as the Eddas, which are good fun. Shop around and look at previews to make sure that you're comfortable with the style of translation.

An anime series of note is the Vinland Saga, although it's certainly not an academic study. If you think of it as a samurai story in Viking-Age dress, you won't be far off.

For movies, Ragnarok (2013) is by far my favorite, if you can get it. It follows a modern-day archaeologist who finds some surprising truths behind viking legends. I also liked Valhalla Rising (2009) for its slow and suspenseful pace (despite the gore), which favorably reminded me of another Arctic movie, The Fast Runner. Valhalla Rising plays on Norse mythology and the Vinland sagas in interesting (but violent) ways.

For music, a number of groups have been inspired by Viking Age poetry and instruments, although we have little idea about how they actually combined these things to make music. I'd recommend (in order) Garmana's Vittrad, Voces Thules' Sturlunga: Battle of Iceland, and Sequentia's Edda.

For children's books, Edda: A Little Valkyrie's First Day of School is absolutely, positively brilliant.

For language, the Viking Language series is remarkably accessible and a good introduction to Norse culture, although it certainly takes a bit of dedication.