"Reading up on lore" is essentially distilling older comics into plotpoints and character spec sheets. This is a good way to familiarize, but reading actual comics (not Wikis) from the 1960's—80's can be very daunting for new readers. I'd focus on more modern stories with dialog/style/setting/tone similar to what you've seen in the movies.
Requesting lore/character/danger-rich stories is a little vague. Can you provide examples from other media to give us a better reference of what that means to you?
Here's my usual copy/paste response to new reader threads:
Forget about continuity, universes, timelines, etc; it's all very confusing, even to creators/veterans. Don’t try to read everything, else you'll be wading through mediocrity for too long. There are so many other great comics (and publishers) to explore!
First appearances/origins aren’t always good starting points. Creative teams change often and characters get re-worked e.g. never caring about Hawkeye until Fraction & Aja’s interpretation. Focus on well-received and relatively self-contained series. Pick an interesting character or team and seek their “greatest hits” stories.
Discover your preferences and let them inform your next comic selection. Do you like older/newer comics? Weird concepts? Super-smart meta-analysis and social commentary? Family-friendly content? Hyper-violence? Male/female protagonists? Humor? Horror? Have you noticed that a specific artist, writer, and/or creative team consistently produces content you like? Follow these instincts.
Marvel Unlimited for digital comics. instocktrades for physical retail (US).
Modern (2000's+) Marvel characters/teams:
Events/crossovers can be tedious. They sometimes intrude on your favorite character series and don’t feel as concise/well-planned. Generally, the best comics integrate these smoothly or avoid them entirely (notwithstanding editorial/executive mandates). Regardless, you may want to read them just to familiarize with major plot points.
Modern (2004-2015) Marvel events/crossovers (in rough reading order):
Welcome to Reddit and Comics.
Just FYI, there's a search bar that where you can type in key words like "new to comics" or "recommended reading" which will return a long list of threads just like this one.
Anyway, here's my usual copy/paste:
Forget about continuity, universes, timelines, etc; it's all very confusing, even to creators/fans. Don’t try to read everything, else you'll be wading through mediocrity for too long. There are so many other great comics (and publishers) to explore!