For NON-gaming computer should I get a Discrete or Indiscrete graphic/video processor?

I have a couple powerful Desktop Gaming PC's and a 6 year old Laptop with a dual core Core i5 CPU and integrated graphics. When I'm surfing the web and watching videos, the old laptop runs just as well as my desktops do. 

The only thing I would suggest is getting a regular sized desktop and not an All-In-One or a Small Form Factor Desktop. Upgrades are either impossible or limited with All-In One PC's and Small Form Factor PC's. Also, I would suggest thinking about getting something with a decent sized Solid State Drive. 

Having a discreet Graphics Card won't make Youtube run better, it won't make the screen sharper, and it won't do anything out of the ordinary with the screen. Now, lets say that in a couple years you get an 8k display. If you want to try to plug your PC with integrated graphics into an 8k display then you would need a Discreet Graphics card that's capable of 8k output, preferably at 60hz. 

It depends entirely on your use case.

If you don't plan on doing anything with your computer beyond everyday use like web browsing, watching videos, and some basic productivity programs then you can get by with integrated graphics like what your processor has built in already.

If you want to do some more intense things like video editing, or you want to connect more than one monitor to your PC then a discrete graphics card would likely be beneficial if not necessary.  But to that end you probably wouldn't need to go out and buy a very expensive one.

i chose a separate gpu because it was upgradable and did so about three years into owning my computer -- modern websites have embedded videos and those eat up gpu power.  i frequently have multiple windows open at a time [16 Gb ram]

Do you do any video or photographic editing? If so, you would still need a discrete graphics card

If you're not going to be doing a lot of gaming you don't need a major video processor. You don't need an external video processor.  But let me tell you something it's always nice to have a computer that has a big replaceable graphics card rather than the ones that are built into the motherboard and soldered in.

That's why I like the Dell m4500 series because they have replaceable components that you can unplug from the motherboard if something Burns out.