Your budget makes it a little tricky, as to buy a great system you would need to spend a bit more ideally! You will need to comprimise somewhere, and the question is where to do that. You have made the right first step though, buying an all in one system will still cost you money, and you will never be entirely satisfied. I suggest not overspending on your receiver, but getting something that offers the features you want at a reasonable price. Don't worry too much about power, go for a reasonable quality brand with the features you really need. There are usually many good offerings with the base model in any range. The advanced models start mucking around with things like airplay, fancy auto setup features, and a bit more power. If you spend it all now on a receiver, it won't leave you much in your budget for speakers, and this would be a mistake. Some people will tell you to go 50/50 between amp and speakers, but I would have to disagree. A set of nicely matched speakers will give you the best start to an enjoyable system for music and home theatre. I would also agree that you are better off spending the money on 3 speakers and a sub ( + reasonable receiver). Add the surround speakers later. The benefits of 3 nice speakers will easily outweigh the benefits of having 5 ok speakers, in my opinion.
Its hard to suggest exactly how you should spend your money, but I would only spend around 300 on your receiver, given that budget. You should push your budget to the 1000 if you can, that will minimize the compromises you have to make. It may seem like a lot, but 600 is also a lot if you are not happy with the result.
I am personally using a 250-300 dollar 2011 model sony strdh820 7.1ch (bought this year), with 3 B&W m-1 speakers (L,R,C), and a B&W asw610 sub. I will be adding 2 more m-1's as soon as I can afford it. It sucks not having it all, but at least I have something to look forward too. The m-1's are a satellite speaker, but I found that they sounded better than most of the bookshelf speakers I tested at that price. They are not quite full range, but also not far off. I'm not suggesting you do exactly the same (this would probably go slightly over your budget), I'm just showing you how I went about spending my cash. I spent 83% of my budget on speakers (including sub), and not regretting it at all. If you are dead set on buying bookshelf's or floorstanders, it may be wise to save a few more penny's first. This is all just my opinion of course, and no doubt some will disagree with me, but I am truly happy with my setup, for both home cinema and music. Good luck, I know it's hard starting out with a limited budget, or a partner that doesn't understand why...
I had both