Like most things...depends. Contrary to what internet gadget guys like to sell, hardwired and shielded is always better. But much more expensive. Underground Feeder ethernet cable is available and can certainly be done with time and money.
But, you might try some wireless systems at that distance first. If, and only if, you don't have anything major blocking straight line signal transmission. Put something in between the antenna transmitter and antenna receiver and things rapidly degrade.
I have done something like you want on the farm at a distance of 350 feet (actually going through some wood and vegetation obstructions). Before you spend a lot of money, you might try something like this:
That unit was pretty cheap for an experiment...and it works. It broadcasts a signal from inside my house to a receiver unit on the outside of my shop. The shop is tin or it might have actually established a signal to the antenna receiver and router inside. If your building is tin, however, you are going to have to do what I did: mount the unit outside (it's allweather), run Power Over Internet (POE) through a bushing to the inside of the building (POE and ethernet power ports are supplied with these antennas), and connect to a router inside and you're off and running.
I have no trouble running a video or getting on the internet to order parts with this system. Now, the box says its for Starlink...well, not so much. Look around on Amazon - there are a lot of these antennas with reviews that don't say Starlink. But, I used a Starlink modem/router to establish a DECO mesh system in an old 1840s brick house with solid brick interior walls. Yeah, you can do that if you have some doorways the signal can get through. Point I'm making is that I wirelessly sent a signal from a DECO mesh "repeater" connected to Starlink's modem/router on the first floor to a DECO mesh unit on the second floor of this house and attached the POE and ethernet cable to the "broadcast" wireless antenna aimed at the shop through a window.
Anyway, it worked fine. And was a cheap experiment to try. I am assuming you have good bandwidth at your house. But...if you have a lot of stuff between the transmission point and receiving point, it might not work. If you live someplace with a lot of possible radio interference nearby, it might not work. This is kinda' old fashioned line-of-sight radio stuff. But, if it looks at all feasible, I would certainly give it a try. Dragging thick equipment tech manuals back and forth to the house for parts ordering really sucks, and I was originally going to put service underground like you implied.
Best of Luck.
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