Can i run it

RX 480-460 or GTX 1060 may work...

with that power supply a 390x is impossible

you may be able to get away with a 480 IF your power supply has the proper pcie cable

the older cpu will also bottleneck it, so dont expect full usage out of it

does your power supply have a spare 6-pin pcie cable?

You have two things going for you: The case and motherboard can accommodate a PCIe x16 GPU. IIRC, the i7-860 can run PCIe 2.0; modern GPUs are PCIe 3.0 but this is backwards compatible. It's totally fine to run at the older version of PCIe.

The only trouble you'll have is with the PSU. Here it's clear that your +12V is split into 3 "rails" which is why it says 12Va 12Vb 12Vc, and they are 18A, 15A, and 8A. Odds are the 12Vc is for the motherboard's 4 or 8 pin connector and should supply you with power on the PCIe slot itself. If your PC currently has a discrete GPU installed, take a look at what cables are going into it. There may be a 6-pin or 8-pin power cable being plugged into it.

Honestly, multi-rail PSUs are an outdated and terrible idea. You'll have almost no idea if you're overloading one of the rails or if you've distributed the load correctly. The best advice I can give you would be to replace the PSU with a single-rail solution. If you had +12V with 41A (18+15+5 = 41), you would not need to worry about this. You'd just need to make sure you had the correct PCIe power cables and if you did then it could work. Here you need to know where each cable came from and what rail it is ultimately connected to. Then you need to estimate what's being run on that rail and whether you're at risk of causing one rail to become overloaded, which can, in the best case, lead to the PC randomly rebooting while in the worst case can cause an electrical fire which burns down your entire house.

Your CPU is still a 4 core 8 thread Intel; despite its age, that 2.8GHz is probably akin to a modern 2.2GHz. This puts it in the high end laptop category in terms of power. Since the high end laptops can run GTX 980s, which are like GTX 1070s, I think you should be fine with a GTX 1060.

Last thing: if you have a discrete GPU, go figure out how much power it's drawing. Whatever it is using you'll know that your current PSU can handle that without a problem. If you find a GPU you want that uses that much or less power and you have the PCIe power cables to handle it then you should be fine.

I agree with all the advice given thus far, especially the PSU, you'll want a decent single 12V rail PSU with a bit more oomph.

Secondly a word of caution. It doesn't happen often, but there is a possibility that you may run into compatibility issues with a new graphics card. OEM motherboards don't always play nice with add in cards, there are cases where they will refuse to POST with certain graphics cards installed. In these cases, sometimes a BIOS update will fix the issue, in other cases, it won't work. That doesn't mean that you can't add a graphics card, it just means you can't add "that" graphics card to the system. I've attended a few threads where this has happened and the OP changed cards to either another manufacturer or different GPU model / maker and they were able to get it to work. So this is just a cautionary post so you don't get blindsided if it doesn't appear to work.

If you use a program like MSI Afterburner and RTSS, you can display your GPU usage in game with the OSD options. Well you can display a lot more than just GPU usage, you can display fan speed, GPU temps, clock speeds, etc etc.