If you are lucky, you could probably still use your rig, just use the Intel HD4000 for the host and pass the 1060 to the guest, but I will be assuming you really want to upgrade to something like Ryzen / Threadripper (cpu without an iGPU).
It’s not advised to have matching cards. You can do it, but you’ll have a harder time identifying which card is which.
As for the host GPU, your only AMD options are RX 460 / 560 or RX 550. I don’t recommend nVidia at all, neither host nor guest (as host, you will have a bad time with nVidia proprietary Linux drivers, as guest, you will have a bad time with nVidia crippling anti-consumer tactics). But if you want to go that route, GT1030 works ok (I got one), while there are also the options of 1050, 1050Ti and 1650. But again, not advisable.
If you go with blue team, you can just use your iGPU as host GPU and save a few bucks, with most probably crippled upgrade path, but I’m not sure if any Intel iGPU has support for DisplayPort 1.4 or HDMI 2.1 yet.
I’d recommend the best AMD card, which is RX 560. But depending on how intensive your task will be, it might not even hit 60 FPS at 4K. Depends what you are doing with it. If you are playing videos at 4K 120 FPS, it should be just fine.
If you aren’t doing anything intensive and want to save a buck, RX 550 will do the job as host GPU just fine.
Oh and btw, at 4K, you don’t want anything with less than 4GB of vRAM. My GT1030 has its video memory almost full even when running full screen youtube. So look for the 4GB versions of these cards.
Additionally, I suggest you look for a PCI-E passthrough friendly motherboard from the beginning, after you decide your CPU (not really a problem with Ryzen). I got lucky with my MSI B250 Pro-VH (I bought on budget and never intended to virtualize, but ended up doing it after 1 year).
Edit: I’m a dummy (and that’s being generous). You can keep your 1060, I thought you were going to sell it along your old rig or something. I’m not sure what you are saying.
Are you asking for a host GPU or a passthrough GPU? The above cards I mentioned as being host GPUs.
If you want to use your 1060 for your Windows VM, you can, you’d have to fiddle with some settings, sometimes in the future nVidia might bork the workaround again with Windows driver updates, but it will work just fine for the moment.
You can also use the 1060 with Nouveau drivers on your host and buy a better passthrough GPU, like an AMD RX 5700 XT, but I’d recommend you stick with passing the 1060 to your guest and using a 560 as your host GPU.