LED monitors are LCD monitors. The LED part just refers to the back lighting. Mainly it makes the back lighting a bit more uniform; nice but not a big deal.
The parts you picked out look pretty decent for a budget gaming computer. The motherboard you listed is not capable of normal crossfire as it has only one PCIEx16 slot.
Hybrid crossfire is crossfiring a discrete card with the onboard video. It can only be done with certain rather weak cards of the HD3000 series I believe and was never particularly useful in the first place, except perhaps on certain laptops.
If you would like to be able to add a second HD5770 in the future you will need a motherboard with 2 PCIEx16 slots, preferably operating at at least x8/x8. Something like this would be a good choice; http://www.newegg.com/Product/Product.aspx?Item=N82E168...
That's actually a pretty good deal for a decent crossfire board. If that's too much just stick with the board you already were looking at and forget about crossfire.
Alternately you could instead change the processor to this one; http://www.newegg.com/Product/Product.aspx?Item=19-103-...
It is Phenom II x2 but it is actually a x4 processor with 2 of the cores locked. The motherboard can be used to unlock the other cores. It isn't guaranteed to work but the odds are actually very good(over 80%.) Check out the user reviews and search for "unlock." You'll see tons of people having success and only a handful that it didn't work for. It is a risk but the odds are good and if you are on a budget you have to cut corners somewhere.