Several of these comics are NSFW due to violence, language, sexual content, or all of the above. Be advised.
Slice of Life Comics
Junior Science Power Hour (web)
Sunstone (Web and print)
Princess Lovepon (web)
Where to get comics on the cheap:
Comixology Unlimited. You get unlimited access to lots of comics, including early issues of series to find out if you want to keep reading them. The content changes, so there’s new things to read.
Go to a big bookstore (such as Barnes and Noble), get a coffee if you don’t plan on purchasing a book, check out some comics or manga, see what strikes your fancy, and consider buying it (or buying the next volume). You can also see what graphic novels and manga your local library offers (digitally and physical). AND ALWAYS CLEAN UP AFTER YOURSELF!
Comixology.com also has bundles and sales.
Check publishers for bundles and sales. For example:
These websites often have bundles of comics and manga on sale. Check back after a sale ends to see what’s new.
Updated comic suggestions from the panel:
The Unbeatable Squirrel Girl
If you’ve never read Order of the stick. http://www.giantitp.com/comics/oots0001.html It is great for all gamers.
Grease space monkeys is also very good. http://www.greasyspacemonkeys.com/comic/in-space
I haven’t read either of those, though I’ve heard a lot about Order of the Stick. Thanks for the suggestion!