So it looks as if, due primarily to the limitations of the PSU in that unit (it's 180 watts, which is
extremely conservative), you'd pretty much be limited to a GT-1030 card. The GT1030 is the type of card I mentioned above, essentially made with these very constrained SFF systems in mind; it's a 30 watt card, which is almost assuredly the lowest-power requirement of any newer (10- or 20-series) GPU.
Mind you, this assumes you're only interested in buying new, current generation. There may be other choices if you're interested or your budget is super tight.
Here's a thread on the HP site about a guy who did just what you're looking at:
HP Slimline Upgrade There are probably lots more like him out there. Although I didn't actually watch them, in my searching I saw quite a few videos about upgrading these HP SFF machines.
The GT1030 should be a fairly big performance advantage over the Intel 610 graphics; anywhere from 200-400% performance. It's a 2G card, so the usable resolution is going to be 1080p or less, but this is probably well beyond what the 610 is doing. Plus, the 610 uses some of your system's memory, leaving you less than 4G - any dedicated add-in card will have it's own memory thus leaving more for the rest of your system.
Will it max out WOFF? No. Particularly not with the CPU you have, since WOFF tends to be somewhat CPU constrained. Will it provide decent performance? Probably. Define "decent"
It really depends on what you're used to. If you've been using the integrated 610 Intel graphics, I cannot imagine you'd be anything but thrilled with the difference even a 1030 could make.
You can find these at most online computer sites (NewEgg, Amazon...) for around $90 depending on exact model.
Also: You'll need to consider what type connection you're using to the monitor. Most common if you're using a TV is HDMI, but there's also DisplayPort and DVI, or even the older VGA - depends on connections on your monitor and cable(s) you already have (unless you wish to buy others). According to the manuals from HP, that model has HDMI and VGA ports on the back for the onboard video.
If you're interested in going beyond what the GT1030 can do, I believe that, technically speaking, you could upgrade the power supply (at additional cost of course) and then support a more powerful GPU; something like the 1660 Lou mentioned above. Those are the most powerful cards (I think) you can get without exceeding the wattage on the PCIe slot itself (meaning the card won't use more than 75 watts.)
(Note that I work far more with Nvidia cards than AMD, so that's what I usually discuss - but this is not to say AMD doesn't have cards that would work. If you're more keen toward AMD, let me know and we'll see what's available).
I hope this helps, and please feel free to ask any questions.