About the power supply, the HP workstations (usually) come with Delta power supplie units (PSU), which are quite reliable in general. If you'd like to see what you have specifically, open the computer and look at the label on the side of the power supply. It will say there.
As for the video card, I had a 600w Delta from an HP workstation and was able to run a similar setup just fine. It had a gtx 780 ti with a gtx 750 ti. I did, however, upgrade the power supply anyway. Running that close to the max power is very inefficient, and also hiccups in power flow from the wall can really throw it off while under load like that. That creates a chance of a harmful surge directly in the PSU. Your surge protector only protects against surges from the wall outlet to the power strip, not against surges that occur directly in something plugged into the power strip.
Even though it's a remote chance that the Delta in your HP will surge (rather than shut down) from being overloaded, I figured spending another $150-$200 on a quality PSU with more power would be worth it in order to protect thousands of dollars worth of components in my computer. I went with the Corsair AX860i. In retrospect I would have been perfectly fine, as I am sure you would be, with the AX760i. However, there are upsides to having extra power.
Power supplies are most efficient (i.e. each watt costs less money to use) when they run at 50% of their capacity. The Corsair AXi-series and AX-series (yes, the "i" makes a difference) both have the highest efficiency of 80+Platinum. That means the AX 760 and AX760i, the AX860 and AX860i, and the AX1200 and AX1200i will all remain at least 90% efficient at 20% and 80% load, and they are nearly 100% efficient at 50% load. In case you aren't familiar with the specialized use of the term "efficiency" in this context, it refers to the ratio of power drawn from the wall (i.e. the power you pay for) to the power the PSU actually delivers (i.e. the power you actually get). PSUs with an 80+Platinum rating will deliver no less than 90% of the wattage that you pay for on your electric bill. For example, if your computer draws 90 watts at a given moment while the PSU is being 90% efficient, that means you actually paid for 100 watts. With a lower 80+ certification (e.g. Gold, Silver, Bronze, etc.), you actually pay for more for the same 90 watts. If you lave your computer on all the time, that can save you more than $100/yr.
Running between 20% and 50% on these power supplies also means that the fan will seldom engage, which means you'll get completely silent power operation most of the time. Also, if you decide to get a GPU that requires additional PCI-e power connectors, you'll likely have to get a PSU anyway. The stock PSUs on HP computers usually have only one set of PCI-e connectors. While the connectors won't be a concern if you get the GTX 750 or 750 ti, the upsides of having a better PSU still apply.
Here are the Corsiar AX- and AXi-series PSUs on NewEgg
The "i" in the AXi costs a little more because it gives you additional controls over the PSU's functionality, whereas the AX gives you no control.