I came out with the results below, but are they fully compatible to each other?
Intel Core i3-3220
ASRock Z77 Extreme4
AMD Radeon HD 7750
Western Digital WD Black 1TB
Samsung DVD Burner SATA Model SH-224BB
Lian Li PC-T60B
Hi. They're compatible but if you're not going to upgrade to a K Series processor for overclocking or extra features, there's no need to get a more expensive Z77 motherboard over a B75 or H77 one. You also don't need an expensive aftermarket cooler when the stock cooler is sufficient. With the money you save you can get 8GB RAM and a better graphics card like the HD 7770, GTX 650 Ti, or even the HD 7850. You also don't need a 600W PSU when you get the CX430 or CX500. Case depends on personal preference so I'm sure you're aware of what you're buying into. What's your budget, system usage and preferred website(s) for parts? Maybe we can help you get the ideal build for your budget.
I wouldn't touch that power supply with a ten foot pole - cheap power supplies are not worth it. You can downgrade the motherboard to an H77 if you're not going to overclock - if you're buying an i3 it doesn't make sense to pair it with a Z77. Then you can use that difference and upgrade your GPU to a 7770 GHz edition or a Radeon 7850.
Here's a couple of things you should be aware of and definitely read before buying incredibly poor quality power supplies: