(1) Processor. I've build some machines with the AMD Phenom II 955. I think it's OK. Customer reviews of cpu at Newegg seem generally favorable:
http://www.newegg.com/Product/Product.aspx?Item=19-103-808&SortField=5&SummaryType=0&Pagesize=10&PurchaseMark=&SelectedRating=-1&VideoOnlyMark=False&VendorMark=&IsFeedbackTab=true&Keywords=(keywords)&Page=1#scrollFullInfo
(2) Expandability. Your take might depend on what you plan to do with it.
You've got a few empty pcie and pci slots. Are you planning to add a highend gpu? Will the psu let you do that? If it will, the psu is still only 350 watts, so you might have some problems if you really decide to load the box up. I think the cpu itself sucks up 125w
You've got room for several more hdd. I'd probably immediately add at least one hdd to use for backup. I'd probably rather have several 500GB or several 1TB hdd than one 2TB hdd: a disk isn't forever; it'll blow some day, and the bigger it is, the more you lose if you aren't backing up
If you're going to tinker with the box at all, check the quality of easily-available manuals for instructions on how to do stuff like that, plus availability of drivers. I didn't search hard, but I wasn't much impressed by what I found on the ZT website. I can't criticize your ethical take on outsourcing, of course, but one thing HP does right is make lots of product info easily available
I can't tell whether you've got more space for more RAM. 16GB ought to be plenty for many purposes. But what's the speed? Did they load up the memory slots with lots of slow memory? If so, what would it cost you to upgrade to faster memory, if you ever decided to? I have one machine I can't upgrade because the RAM is unbelievably expensive: the mfr stuffed the slots with the smallest possible sticks, so I'd have to pull and replace them all for an upgrade
(3) OS. You paying for Windows Home Premium. Meh. OK. Maybe you need it or maybe you just like it. If I added several hdds, I'd probably at least install Ubuntu on one of them
(4) The machine comes with bloatware ...
... including a trial for Symantec Norton Internet Security. My Norton experience wasn't happy. I'd use something else: Microsoft Security Essentials is free.
The bloatware is also gonna try to hook you into shelling out for Microsoft Office down the road. I'd resist unless I really really needed office. Check this out first:
http://www.theopendisc.com/