"USB internet stick" doesn't sound like much. That sounds like a device designed to connect to a single computer. The starting point is to ask for an ethernet connection that I can connect to a router. That could be, depending on the ISP and other factors, a box that takes the exact same "USB internet stick" that you already have and provides ethernet output, or it could be a box that has everything (4G antenna/transceiver, ethernet connection, possibly even a full router0 all in one.
Once you have that, you now have either a single ethernet connection (connect it to a router to share with multiple computers, WiFi hotspots, etc.) or multiple ethernet connections (if they include a router as part of the "magic internet box") in which case you just pick one of those ethernet connections.
Now you have two challenges:
Power
Assuming you don't happen to have power on the hill (no, not political power on Capitol Hill...), you need to provide power to this device. Regular Power over Ethernet won't help you much, not at 350 meters, but there are some PoE extenders available that might do the job, depending on power requirements.
But if PoE won't work, then since power loss over 350 meters is huge, especially at low voltage (and at high voltage you run into other problems), that may mean setting up a small off-grid self-contained system. Typically that means:
- Batteries (designed for a couple of years worth of daily charge/discharge cycles, capacity dependent on daily power requirements, ideally so that on a typical winter day and after a couple of years of expected use you only normally discharge to around 50%)
- Solar Panels (designed to fully charge batteries every day based on expected usage and seasonal variations in time/intensity of sunlight)
- Battery Charger
- Converter (the technology will vary depending on required output AC vs. DC, voltage, etc.) to produce the necessary power for your modem/router/etc.
Network
USB only goes a few feet. More importantly, standard ethernet is designed for 100 meters, and you need to send a signal 350 meters. There are basically three methods to span a long distance:
- Copper Wires (coax or twisted pair)
You won't get Gigabit speed, but you can certainly get connections fast enough for normal internet use. The wire (cable really) is relatively inexpensive. However, you will need to either get direct-bury cable and bury it or use conduit (and possibly bury that too, at least for portions of the run) to protect from critters and weather.
The cable tends to be more expensive, and putting the ends is not as trivial as with copper (but you can get long pre-assembled cables) but the same issues of bury and/or conduit apply as with copper. High speed available.
Note that I did not say "WiFi". Traditional WiFi is not going to work well at 350 meters. But there are other wireless schemes available. There may be licensing issues (depending on the type/power/frequency) and equipment may be expensive. But you don't have to worry about 350 meters of cable having problems.