I grew up reading early because of comics. I did read appropriate ones with my children, but also read a lot of novels to them (Harry Potter for instance.)
It felt strange to find that their favorites were not mine. I did find that smaller publishers did better with them than Marvel and DC.
My daughter loved titles like "Elf Quest" by the Pini's.
My son liked "Dynamo Joe"
You are lucky that many comics are available cheap or free on the internet, but appropriateness varies sharply. I have quite a few in the iPad Comixology app, which has deals with both DC and Marvel as well as others. (You can get more freebies in Marvel and DC's own apps however.)
With electronic comics, there is no collectible, but it usually is cheaper. And you can share without worry about anyone destroying a paper collectible.
And of course, you can get huge collections on the cheap via ebay and Craig's list.