Doesn't make sense to buy an APU with integrated GPU, and then pay for another discrete GPU. Unless you need to drive like 9 monitors or something. Either pick the APU without a discrete GPU, or, if the budget allows, pick a CPU + discrete GPU. The 760k X4 for example, would be a good chip to pair with an HD7850.
It wouldn't make sense to buy an Athlon X4 750k, and then buy an HD6570 DDR3, and then buy an HD7850, but that is very nearly what is happening when one purchases an A10-5800k only to then disable the iGPU and use it with a discrete GPU anyway.
The Zalman CNPS5X is a great little compact cooler for the money that often solves a lot of problems on AMD boards because it is one of the few that will mount parallel to the DIMM slots, so as not to cover them up. (and is easy to install and a pretty good performer for it's size) That said, it is always a good idea to carefully study pictures and diagrams and dimensions of the board and CPU cooler before purchasing any after-marked cooling solution to ensure that it will in fact fit without interference. Over-head pictures of motherboards, and a program like gimp, along with a calculator can be used to get fairly accurate "measurements" of spacing around the cpu socket (use the board dimensions to extrapolate dimensions to slots/components, etc)
You can probably skip a sound card. The motherboard will have pretty good onboard sound, and if it concerns you that much, Biostar has a "hifi" oriented line of boards worth looking into. The money spent on a sound card would be better spend elsewhere unless you have a specific need for a function of said sound card (OI related musical creation something?)
You don't need an ethernet card. It is built into the motherboard.
The FM2A75 is now outdated. Consider something like the ASRock FM2A88X
There's almost always a reasonable quality 1080P 21-23" LED-LCD monitor on sale for around $100. Doesn't make sense these days to buy smaller or lower resolution than this new. This is the "buy-in" point that makes sense, otherwise go to a local thrift store and buy their used sub-HD LCDs for $25.
While 350W is technically enough power to run the system, having enough wattage alone does not always guarantee that it will work. The 350W Antec Basiq is based on an older topology, that better suited the power distribution of older PC hardware. These days, almost EVERYTHING in a computer is powered by the 12V rail. The ole Basiq actually only has "276W" available on it's 12V rails, and that's only if a load is presented that matches the dual rail configurations balance. (unlikely). Realistically speaking, it would be hard to utilize that PSU for a build that could draw more than 200W because the odds of being able to balance the load on the dual rail design in such a way so as not to overload it, are poor at best. Furthermore, the Basiq is a low efficiency, hot running PSU with small, high speed (noisy) fans [compared to modern offerings].
A 100W TDP CPU, combined with a 130W TDP GPU, +drives, +RAM, +south-bridge, +VRM losses on the motherboard, +sound/usb/fans/ethernet/sata-controller etc etc etc... It would not be unreasonable to figure that such a machine could at times, pull up to 300W.
Here's an example of a 350W PSU that has enough power and flexibility available on it's 12V rails to power this machine: http://www.newegg.com/Product/Product.aspx?Item=N82E16817151077&nm_mc=AFC-C8Junction&cm_mmc=AFC-C8Junction-_-na-_-na-_-na&cm_sp=&AID=10446076&PID=3938566&SID=
Though I still would suggest a different route....
I suggest a 400-500W PSU, something with a 120mm or larger fan, dedicated (included) 6+2pin PCIE power connectors, single 12V rail (if possible) and 80+ bronze efficiency or better from a reputable name or OEM. I usually suggest either the FSP Aurum S 400W, or the Rosewill Capstone 450W for budget builds.
Best of luck with the build,