g-unit1111 has a great response, showing that it can be quite easy to build a better machine. In fact you could save even more by being more modest with parts, and deciding what to do with the savings. For instance (prices from Newegg):
$200 27" AOC e2752She monitor (not touch enabled)
$190 Intel i5 3470 processor (quad core, MUCH faster than i7 series in the HP)
$048 MSI H61M-P31/W8 motherboard
$075 8GB (2 x 4GB) Avexir AVD3U1600 RAM (12 GB is not necessary for almost anything that HP would do)
$085 1TB Seagate Hybrid ST1000DX001 harddrive
$100 Win 8.1 -64bit
$014 TPLink TL-WN722N USB WiFi dongle with antenna
$023 Logitech combo keyboard & mouse, wireless, MK270
$120 EVGA GeForce GTX750 (512 desktop cores vs. 384 laptop cores on HP) 01G-P4-2751-KR. WAY FASTER.
$855 Total (savings to be used to by case of choice to create small form-factor, tower, HTPC, mini-PC)
Also, for a small sum ($80) one could add an SSD to this rig, with much faster boot times and better performance overall. Now building it should be done by someone with some experience but its not that difficult, and there can be much satisfaction in building it oneself and understanding what goes into it. This rig would also allow for some upgrades in RAM, and in graphics cards, offering more growth than the all-in-one.
In short, with the right help and guidance, you can do much better, but it means you are the warrantor of the build, and you need to be involved in its maintenance and operation.
JG