Comico, which is an online daily serialization magazine and the manga are free to read
You could also check out the free (無料) section on manga sites like ebookjapan:
^some are free to read for a certain period of time, some are free to download and keep forever
As far as recommendations go, よつばと! is a popular one, it has its own discussion threads for questions here on the forums, as well as other suggestions like Shirokuma’s Cafe (currently being read by the Absolute Beginner’s Book Club), Chi’s Sweet Home, etc
There are varying levels of Japanese book clubs here, I’d recommend checking out the Master List of Book Clubs here to see what’s been done/ongoing to see if you want to jump in, or even checking out previous nominations at the different levels (i.e. Absolute Beginner’s or Beginner’s book clubs) to get ideas for suggestions
Happy reading! 
