Editing webtext is like editing poetry. Space is essential, so every word has to hold its own and be the best choice.
Kilian makes some fair points and has some nice lists in chapter five of Writing for the Web. I'll share some pointers of my own.
To edit your text, move it into a new word processing document. Swap the font out and mess with the layout. Then let it sit. Don't look at or think about it for a while, and it'll be fresh and new when you come back to it (and see all your mistakes!). Kilian suggests printing it out, double spacing, increasing the font size, and changing the font. However, I don't see a reason to have to retype all those changes and waste paper. Then again, I grew up using computers so I'm more comfortable editing on screens.
A large section of the chapter lists abbreviations and terms for web writing. My advice: if you have to look it up, don't use it. If English is your second language, check out resources online or get a hard copy text to refer to. This is a nice start and easy skim list, but I'm not really sure how useful it is in the long run. Depending on your major and the purpose of your website, most of the stuff on this list you'll never run into - and you could easily do a websearch for it if you did.
Kilian also gives some advice that can be boiled down to the following: don't be an offensive jerk, don't ramble on with unnecessary junk, watch out for confusion from dialect/terminology if you have a global audience, and hyphenate to avoid confusion if you must.
Just don't sacrifice your style for the sake of appealing to a larger audience. Most websites get little traffic. Find your niche and write what your fans want. If you get famous, then you can think about appealing to huge audiences... but realistically, you probably won't get so much traffic that you have to worry about it. Just be an accessible, not-outrageously-offensive version of yourself.