I have only ridden a fixed gear road bike once. It was weird and I didn’t really like going fast because you have to somehow slow your legs down to slow the bike down. I ride a single speed and geared mountain bike.
Gears: Able to find the right one for the trail or road you are on to either spin up a hill or fly down it; more expensive to maintain; more things to go wrong on the trail
Singlespeed: no worries about switching gears to find the right one; fly up the hills (if you are fit enough); sometimes run out of gear on the flats or downhills; not much can go wrong on the trail and you can bring what you need to fix a broken chain to get back to the trail head; cheap
A single speed mountain bike can go anywhere one with gears can. I have ridden my single speed in Maryland, Delaware, New Jersey, Pennsylvania, Vermont, New York. There are places that I prefer the bike with gears, but that is a function of my fitness, not because of the bike.
One of my riding buddies, 53 years young, only rides his single speed. He kicks the rest of our asses, no matter what or where we are riding.
We met riders at a bike festival in the Shenandoah Valley that were riding single speeds. And those were the hardest trails that I have ever ridden.
I’ve ridden in Waterbury, Vermont (the best cross country trails I have ever ridden) with guys on single speeds.
I don’t think I would recommend starting with a single speed, but man, are they fun to ride.