I know this is a somewhat old thread, but I happened across it while having a look around.
Personally, I use and actually like MS Word. It does everything I need to do and it's a piece of software that I'm quite familiar with.
I've used Open Office a bit and in all honesty, it would probably be find for what I do, but I see no reason to learn new software when what I have works just fine.
As for spelling and grammar, Word does in fact check both, but software can only do so much to help the helpless.
If you say spell, won't as want, there's not a spellchecker on the planet that is going to catch it. A grammar checker might, depending on the context, but I've seen a grammar check miss obvious errors and I've also had grammar checkers tell me something was wrong when it wasn't.
Avatar is right about the best way to learn. You learn to write good English, or any other language, by reading well written books in that language.
Also, in the case of English, buy and actually read a copy of Stunk and White.