I work in graphics and print. We use Indesign all the time.
You did right not to go with Quark - it's outdated and expensive and they're so many compatiilty issues its not worth going into.
You're doing an e-zine so you shouldn't have a problem with the following BUT if ever you want to go to print read on...
If you're sending a printer an Indesign file make sure you give them a
HiRes, Print pdf with fonts embedded. If they ask for the native Indesign file you must ensure the printer has all the fonts and send them the 'Live' file.
However.... if the printer asks for the Indesign file with 'outlined' (or vectorised) fonts be very very wary!!

if you outline the fonts in an Indesign file you run the risk of losing formats such as underlining and text boxes!!

The only way around this is to create all these lines by hand which is an absolute ball ache, especially if text is amended and then reflows. This would mean having to amend & check every line individuallly.
A printer wouldn't do this for you unless they were a) being paid b) stupid
Use this thread for any Indesign queries you may have - I'm sure someone will help.
Also try the Adobe forums as there will be an Indesign specific one there. + many other graphic App forums online if you search. (don't use Google forums tho')