1. yes, the antec 300 is a great case. I only chose the soprano, even though it is older, because you wanted a window and lights and I thought it looked a little better. Just my personal preference though as I like silver over black.
2. I think it is a great idea if you know what you are doing. Overclocking is a great way to squeeze extra performance out of a processor for not a lot more money (just the price of a cooler). With that processor, you could most likely get to 4.0 GHz without much trouble. However, if you are not sure what you are doing, you can really mess it up too. Be sure and read the guides on the forum. In my recommendation I have a Phenom Black edition processor. That means that the process of overclocking is easier for that particular processor. Start by reading this sticky:
AMD Black Edition Overclock (by Raising Multiplier) Guide
3. The easiest way to answer that is to just look at benchmarks. This link to anandtech's review of the 6850 an 6870 cards includes the 5770 in the benchmarks. Here you can see how it stacks up at 1920x1080 resolution.
AMD’s Radeon HD 6870 & 6850: Renewing Competition in the Mid-Range Market
4. www.microdirect.co.uk There may be better sites, but I am not familiar with them as I live in the US and always use newegg.com
5. Again, this is where benchmarks come in. Look at both tom's hardware charts and anand's bench section (anandtech.com) and compare your graphics card to the other ones listed and your CPU to the others. Look for specific apps/games that you will be using and that should give you a good idea. Personally, I think it is a good build, especially in this budget range. This month Tom's did list the 5770 as the best graphics card for the money and described it as "Great 1920x1200 performance in most games" but looking at the benchmarks, don't expect to play games like stalker, crysis warhead, and BC2 at max settings AND AA enabled. I think it would provide outstanding performance on a 22"1680x1050 monitor.
6. Just realized that I didn't include a Hard Drive in your build. I would go for the samsung spinpoint F3 500GB or 1TB model. To fit it in your budget, you might have to drop to the Athlon x4 640 which is still a great processor, just no L3 cache which can have a small effect on performance. Check out this article for info on that
Athlon II Or Phenom II: Does Your CPU Need L3 Cache?
Also, I just checked the recommended gigabyte board on gigabyte's website and it doesn't have x8/x8 crossfire. I would probably go with either the asrock extreme3 or the gigabyte ga-890gpa-ud3h if you want to crossfire. This is why a second opinion is always welcome. You never know what little detail you might miss that a fresh set of eyes might catch.
7. Please do. These are just my personal opinions on what I would build. Others might have completely different ideas. To give you an idea of where I am coming from, I just built a computer (last week) with a Phenom X6 1090T, Same PSU, very similar motherboard (Gigabyte GA-890GPA-UD3H) with 4GB of OCZ ram, Samsung spinpoint f3 1TB HDD, and a xigmatek Gaia cooler ( I would recommend this one if you can find it over the coolermaster 212 because it mounts for crossflow ventilation. I just couldn't find it on the site I was using. They both perform virtually the same though. Just the direction of air flow is different.) Best of luck building and feel free to ask any other questions you might have.