Direct burial is a mistake, IMHO and IMProfessional, less H, O. Trenches are expensive, conduit is cheap, and things with teeth that burrow can and do find direct buried cables. Dig the trench once.
Fiber is far preferable to wire for electrical isolation alone, not to mention potential capacity, if ever needed.
In most cases (shopping is off-topic and I haven't shopped lately) a small switch (4-8 ports) with an SFP or SFP+ slot is less expensive than a "media converter" - unless you need a larger switch anyway, then get the size you need with SFP or SFP+ slot(s).
The usual constraint for home projects is termination - you either need conduit large enough to pass a pre-terminated cable, or you need to hire someone to come terminate the fiber, or you need to invest a good deal of money and time in becoming equipped to terminate the fiber yourself. I did the latter on a "non-home" project where it paid off to the tune of 10's of thousands of dollars, but that won't be the case for 2-4 terminations at your home.
My personal recommendation on fiber is to use single-mode (9um core) not multimode (50µm core, or severely outdated/slow 62.5µm core) - "used to be" the SFPs were far more expensive for single-mode. That price dropped a lot, and decent multi-mode cable costs MORE than single-mode cable. Singlemode has essentially no speed limit, while multimode has sharp speed limits.
Be sure to use cable rated for wet locations. An indoor-type patch cord may work for a while, but it will fail eventually in wet service. "Drop" cable may be particularly good for the purpose, as it's designed for "pole to house" service and somewhat more rugged than the average fiber cable to withstand handling. Be sure to get the fully non-conductive sort (no tracer wire, or removable tracer wire that you remove) if putting it in with the power wiring. "All Dielectric" is a term that means the same (Usually seen with ADSS - "All Dielectric Self-Supporting" which is commonly more expensive than drop cable, even though the drop cable is technically also self supporting and all dielectric...since you are putting it in conduit (or the ground) you don't need self-supporting at all.)
Get whatever works out best when you shop - you can do it on a single fiber with "bi-directional" SFPs that use different wavelengths, or the more normal 2-fiber method. But you may find 6 or 12 fibers costs no more, or even less.
RBR (reduced bend radius) fiber is typically available for almost no cost increase from a good cable supplier, and makes the fiber installation much less sensitive to how tightly it's bent (the sales-dudes like to wrap it around a pencil.) Don't be a sales dude on your install, but if you can get it without an absurd up-charge, it's better to have it than not.