We use Spiceworks for I.T. - Free, simple setup , lots of features (a good number we don't use) and a large helpful community. Takes some horsepower on the server side if you want it to be snappy, but nothing unreasonable. We have 1.5 IT guys as well
We've used OS Ticket for facilities and publications in the past, it does well and is free too. It wasn't my favorite, for some reason we had trouble getting the cron jobs to work reliably - Spiceworks has been much more reliable but way over featured for facilities/publications. We're actually working on doing this through RockRMS now, but I don't think workflows trigger from emails yet which is what would be ideal for our situation.
I have no idea what is available in Office 365 to meet that kind of need.