All of the primary tests were performed with Windows 7 and Internet Explorer 11 (except for Keynote for iCloud, which I ran in Chrome). I also ran a series of secondary tests using a wide array of operating systems and browsers.
Take it from the topMicrosoft's Office Online (known as Office Web Apps before February 2014) works with any recent version of IE, Firefox, Chrome, or Safari. It's free for personal use. Individuals and organizations with Office 365 subscriptions (from $60 to $240 per person per year) automatically get licenses to use the Office Online apps. If you're familiar with Office 2010 or Office 2013/Office 365, you should be able to jump right into the Office Online apps and get going.
While Microsoft packs a great many useful features into its Office Online suite, I was most disappointed by three problems. First, in my tests, Office Online bungled several Office documents -- real ones, gathered in the wild. The damage included a Word doc with a simple formula, an Excel spreadsheet with macros, and a large Word document consisting of photos and text boxes that, when opened in Office Online, then saved, was completely mangled. Word, Excel, and PowerPoint Online won't even open password-protected documents.
Second, the Office Online interface is still staunchly old-school Office. There's been no attempt to borrow from the excellent Office for iPad efforts. That means, among other things, you're visually bewildered by many choices that don't do much.
Third, PowerPoint Online is both buggy and severely limited. It might be useful for creating a very simple presentation or sketching out a presentation you'll flesh out later in desktop PowerPoint. But I wouldn't trust it to edit an existing presentation.