I'm not sure how high-end a card you could use in this system, with the PSU and size limitations, but you'd need a low-profile card that doesn't eat too much power - I think the best you can do is a special low-profile/low-riser card using the Geforce 1030 or 1050. 

https://www.amazon.ca/GIGABYTE-GeForce-GV-N1030D5-2GL-Computer-Graphics/dp/B071DY2VJR/

Something like this seems to be a popular choice, just make sure that a) the card you want is a low-profile card with a half-height bracket/backplate and b) there is no external power connector as the SFF won't have it or support the extra power draw.

The video output are the 2 DISPLAY PORT connectors.

https://www.dell.com/en-us/work/shop/accessories/apd/470-aanj

You could add a GT1030 which would give you HDMI and DVI.

8CCF1 GeForce GT 1030 has the following video out ports = DVI-D SL/HDMI

DELL OEM GT1030 

NON DELL CARDS will require SECURE BOOT OFF and LEGACY ON.

https://www.dell.com/en-us/work/shop/accessories/apd/a9763687/

https://www.youtube.com/watch?v=2y32mBdZHJY

https://www.dell.com/en-us/work/shop/accessories/apd/490-bemx

MD Radeon R5 430 Low Profile 2GB (DP/SL-DVI-I)

Manufacturer part 14YV0 / 00F8PX Dell part 490-BEMX

Amd R5 430 full height 2gb

https://www.dell.com/en-us/work/shop/accessories/apd/490-bdlo

OptiPlex 3050 (MT), 5050 (MT), 7050 (MT) Manufacturer part H7WJ3

Validated Dell OEM video cards = VVYN4, D7DYD, 2C7NH

AMD Radeon HD7470 0WH7F, N1N66, NFXD5, 2FVV6

AMD Radeon HD7470 Low profile 9M4KG, NJ0D3

AMD Radeon HD7570 KFWWP, 4C5DK

AMD Radeon HD7570 Low profile

YG17P Nvidia GeForce 640GT

MSI GTX 1050TI LP IS THE BEST CARD THAT YOU CAN PUT IN THIS MACHINE.

https://www.dell.com/en-us/work/shop/msi-gtx-1050-ti-4gt-lp-graphics-card-nvidia-4-gb-gddr5-pcie-30-x16-low-profile-dvi-hdmi-displayport/apd/aa362024/graphic-video-cards

Graphics Options2 Integrated Intel® HD Graphics 630
AMD Radeon™ R5 430, 2GB
AMD Radeon™ RX 550, 4GB
NVIDIA GeForce® GT 730, 2GB
NVIDIA GeForce® GTX 1050, 4GB (Tower only)
Dual AMD Radeon™ R5 430, 2GB
Dual AMD Radeon™ RX 550, 4GB (Tower only)

So  does GTX 1050TI work in Optiplex 7060 Mini Tower XCTO with 260W 92%?

welcome to DP ,display port, its really great.

buy monitor with DP

buy and adapter  plug from DP to what  ever yours is, DVI ?

or spend weeks tying not to over load that weak gutless PSU with 10 cards failed

why buy any SFF is the question I have, why do that?

I have kit box in the lab here that adapts anything to anything, all work, some sold 12,000 miles south west are no good, sold for $3. some even lie.

YOU SAID NOT GAMING SO I BELIEVED YOU.

https://www.dell.com/en-us/work/shop/cty/pdp/spd/optiplex-7060-desktop

75W cards require power supply OUTSIDE of the Case because the "TOWER" is actually sub compact very similar to Inspiron 3650.

Power 24 Pin to 6 Pin Adapter Cable

https://www.moddiy.com/products/Dell-OptiPlex-3040-3050-3060-Main-Power-24-Pin-to-6-Pin-Adapter-Cable.html

https://www.youtube.com/watch?v=SCQTj1ei3Ew

no monitor at all just TV i guess,

same link same place but TV HDMI out.

DP to HDMI

sold everywhere really. and is SUPER COMMON this. as many PCs do  not have HDMI at all.

the only tricky adaptations (besides omg thunderbolt)

are (DP has 500mA of power) HDMI is super weak, so when adapting HDMI to other things

make sure the adapter has USB power stealing cable. or it will not work, with 50ma power pin hdmi 10x less.

but you are not doing HDMI to other things,

so yours is EASY as pie. 

No idea why you say that.

https://www.dell.com/support/home/us/en/04/product-support/product/optiplex-7060-desktop/docs

https://topics-cdn.dell.com/pdf/optiplex-7060-desktop_service-manual2_en-us.pdf

low profile card fits fine

https://www.youtube.com/watch?v=2y32mBdZHJY

https://www.dell.com/en-us/work/shop/msi-gt-1030-2g-lp-oc-graphic-card-2-gb-gddr5-pcie-30-x16-low-profile-hdmi-displayport/apd/aa362018/graphic-video-cards

The GT1030 does not fit in 7060 sff