Raikas said:
One thing I'd warn you then (if you've genuinely not read many comics before) is that serialized team superhero books tend to have a distinct soap opera flavour - it's just the nature of ongoing serialized fiction with large casts. There are some that avoid that, either because they're deconstructions (like Watchmen) or reinventions (like The Invisibles) or just side-books (like Planetary). I'm a fan of the genre myself (my avatar probably gives that away), but I've found that a lot of people are surprised when they get into it via TV and movie adaptations.
Based on your TV bits: If you're into crime stories, I'd recommend Ed Brubaker's Criminal, Fatal, and Scene of the Crime.
For Fantasy, Sandman is classic and lots of people like Fables. And Saga is a brilliant current title. There's also a lot of great SF/F work in French comics and manga - are you looking for recs there too?
Good stuff. Some other pieces of advice off the top of my head:
1. I'd recommend keeping an open mind to the world outside Marvel and DC superheroes, I enjoy some of these and obviously so do a lot of other people, but there are smaller publishers like Dark Horse and Dynamite who make neat stuff in other genres.
2. Be aware that particularly for modern superhero comics, there's a lot of backstory and a lot of crossover between books, it may be hard to follow a story sometimes reading just one series.
3. Try international. The more contained format of mangas and manhwas leads many people to prefer them over western comics. To say nothing of British comics like 2000 AD, which most famously in the US is the home of Judge Dredd.
4. Familiarize yourself with the different "eras" of comic books. Generally speaking, the further back you go the sillier and more old fashioned the stories get. There's some disagreement on the names and exact dating of the lesser ages but most agree that broadly speaking the 1940s is the "Golden Age" and the 1960s is the "Silver Age".
5.
Most importantly. Buy trade paperbacks (at least to start) not single issues. Trades are where you get the most bang for your buck in comics. And they're the best way to read up on the history of a character/series you like without breaking the bank.
For example you mentioned "The Avengers #1 reprints" you can get "The Essential Avengers #1" trade paperback which has about 500 pages of
black and white reprints of the series, with the first 24 issues. Or spend a little more to get "Marvel Masterworks The Avengers volume 1" which has the first 10 issues of the Avengers in glossy color reproduction.
Trades will also often contain an entire storyline/story arc which was originally published in 2 or more comic series, saving you from having to hunt down issues of a series you're not subscribed to or read a synopsis online to follow an onging storyline
Be aware that the hobby can become a money sink very easily. A good way to test out series/characters without wasting money if you have a library that participates in inter-library loan is to request that your library borrow trades you're curious about. worldcat should provide you with the information you need for this. http://www.worldcat.org/
Lastly (at least until you confirm you're looking for series suggestions lol) if you do wind up getting into comics and want to collect single issues you're going to want some of these:
http://www.amazon.com/BCW-Brand-SHORT-Comic-Storage/dp/B005N1HA1S/ref=sr_1_2?ie=UTF8&qid=1391669256&sr=8-2&
http://www.amazon.com/BCW-Current-Comic-Book-Boards/dp/B001244X56/ref=sr_1_3?ie=UTF8&qid=1391669292&sr=8-3&
