The games themselves are just standard arcade-style games, of the sub-genre of shmups called "bullet hell", where enemies attack in very wide spreads, attempting to make you nervous to move a lot and fail to see safe spots. While it's a genre usually based on skill, it has a bit of a puzzle element.
Touhou games are usually fairly accessible at low difficulties and very challenging at high difficulties, and special stages you unlock when clearing the main game.
Although there has been like 17 games in the series, the developer is usually adept enough to bring enough gimmicks and scoring systems to the table to keep it fresh, but not overly complicated. Dude clearly loves the genre and there are lots of references to classics hidden away.
Basic setup is six stages. With the first two stages being a warming up with little relation to the story, then stage 3 kicks it up, stage 4 has a gimmick boss, 5 has the most variance, and 6 is the climax with the final battle. Then you unlock a very difficult extra stage, but that's optional and is run separately.
You usually get a couple characters, with a few different modes each, or a wider array of characters with more specialized shot types and speeds, so you can easily find a setup you like.
The characters are indeed mostly all female, but there's no sexy times, innuendos or rape backstories to be had. While they wear weird victorian-esque clothes, there's hardly any skin showing, no mention of boob sizes or any of that stuff, no ship teases, no romantic subplots, nothing. It's just girls with weirdly elaborate clothes based on folklore beasts. The only thing that doesn't warrant it a family-friendly rating is that some of the characters are evil and eat people, and there's a bit of a grim subtext in places.
There are a few characters that are intended to be young-looking, but the "1000 year old dragon loli" trope is not really invoked. Those characters also tend to be written to be really obnoxious despite looking cutesy, so the author is not really idealizing loli (if nothing else, it seems to be a jab at the concept, pretty much every childish character IS childish in a bad way). The thinking every character is a loli is just because the developer sucks ass at drawing, giving everyone very round faces and no curves (which would be hidden away by the dresses anyway), but now that he has developed more skill it's more obvious the characters are hardly ever lolis. Male characters exist, but they usually take the role of mentors or companions and are notoriously not fighters except for one (a sentient cloud creature).
Now, the canon is loose, but it's not non-existent. Characters tend to have more detailed profiles included with the game disks (since everyone pirates the games, no troon knows it's a thing). The tone is a bit all over the place, with some characters being silly and hardly threatening while others are played seriously or for drama.
The general setting is about an isolated dimension where things forgotten by humanity end up at. It's mostly populated by a mix of folklore creatures (not limited to Japanese ones), as well as the spirits of the deceased and supernatural forces and whatnot. The "real" world in this setting is more industrialized and gray than the actual real world, discarding beliefs and customs at a faster rate than us, but that's only touched upon in some novels.
To put it short, the world in the games is some sort of nature reserve for folklore. Some take on human forms, since those creatures are more spiritual than physical, but they can also come in more traditional monstrous-looking forms (those rarely appear in the games other than as basic bitch enemies, barring that cloud creature).
Since it's a nature reserve of sorts, combat has been reduced to a game to keep things as non-lethal as possible (but that's not a rule that applies to outsiders that wander in).
The main characters are Reimu, the one designated as pretty much the sheriff of the place, and Marisa, a witch with terrible manners but puts effort into things. Both of them are young adults (more noticeable when canon works have a guest artist). Despite fan interpretations, Reimu is a hardass that shoots first and is not highly personable, and Marisa is rude and has long fingers but she's not a walking meme. They fight crime (basically powerful enemies making a ruckus that threatens the stability of the place, either intentionally or not).
Now, ZUN, the author, is not particularly interested in keeping some sort of purity of the lore, so he gives no real fucks when someone does fanworks, fangames or whatever with his characters. It's a side gig to him, as he works in the actual game industry for a living. That kinda decision is what set the foundations of horror.