I'd be loath to run Ethernet over copper between buildings, because of the possibility of different ground potentials and other related issues. If it was me, I'd buy a
pre-terminated OM4 armoured fibre assembly with LC connectors (probably
Steel Wire Armoured, which can be buried straight in the ground, though other armour options are available). You run the cable between the buildings, remove the end caps and click the individual fibres into LC-LC couplers inside a
patch box or patch panel. I'd go for at least four fibres in the assembly, which gives you a second duplex pairs for redundancy.
Once the fibre is in place, you use
OM4 LC-LC patch cables to connect to the optics. 1000Base-SX will be more than adequate for your needs; there's no point spending a fortune on a 10Gbit/s link, though the fibre itself is capable of 10Gbit/s. If you just want to connect a single device, you can get a media convertor, otherwise use switches with SFP ports for the 1000Base-SX SFP optics. These need not cost that much - I would shop around for the switches and SFPs.
The links are to Universal Networks, with which I have no connection other than as a satisfied customer.