1. Get a better CPU. His current Pentium is not that great. From the CPU list on that site, an i5-2500 would be a huge upgrade (putting him pretty much even with AMD's FX chips), while an i7-2600 would put him at the top of the list (http://www.tomshardware.com/reviews/cpu-hierarchy,4312.html) -- depending on the game or app, he'll either see equal performance to the current i7s, or maybe only lose 15-20% performance.
2. I'm assuming he has 64-bit Windows (otherwise 6GB is useless to him anyway). However, with that RAM it means he has a 4GB & a 2GB module, which means no dual data channel capability. He's got 2 DDR3 slots, so I would recommend finding a 2x4GB set of DDR3-1333 memory.
3. His PSU is going to hold him back from top-line upgrades. However, this is an HP OEM build, so I doubt his monitor can even hit 1080p resolutions. So, unless he wants to replace his PSU, his best bet for a GPU upgrade is going to be the GTX 1050: it's good-to-great for 1080p resolutions (which means it'll rock anything from 720p up to 1600x900 resolutions), plus the base models don't need PCIe power connectors from the PSU (which I doubt his PSU has); they just draw power straight from the PCIe slot on the motherboard, & only need a 300W PSU. If he can't find one of those available, he should look for one of the low-power GTX 950 models (previous generation)...or, if he can't find either of those, I suppose a GTX 750Ti would be an "OK" upgrade (it's not "great", but it's way better than the Intel integrated graphics). And yes, it's only PCIe v2.0, but the x16 slot will have more than enough bandwidth for the GPU.
If he can also afford a PSU replacement (& assuming he can find one that matches the current PSU's form factor), a nice solid 550W will let him get an RX 470/480 or GTX 1060 instead. Unless he's replaced the monitor, though, I don't think he's going to need that kind of GPU horsepower.