As long as the PC you're speccing out isn't a slimline, then you can add a HD4670 for about $70 and will be fine with the power supply that comes with the HP. The GT 230 is basically a rebranded 9600GT (check the chart to compare)
Unless you order the actual "slimline" then the card would work. All the cards will fit in the HP p6180t. The limiting factor in HPs is their power supplies, it will come shipped with a good quality 300w power supply. Since the 4670 only uses about 50-60 watts of power and does not require a 6 pin PCIe connector from the power supply it's a good match up for the system and your uses for it. If you want to get a higher powered graphic card for the system you'd probably have to get a new power supply or try to order one with the system. Either of the 2 you had listed would be fine, you may want to check warranties.