Congrats on your new horse. You should also take a moment to pop by the Gaited Horse section of the forums if you haven't already!
While it is difficult to event most gaited horses with non-gaited horses, I recommend you embrace your horses natural gift. You mentioned you want to ride just for fun, when you get out on the trail, you are going to be blessed by having the smoothest horse in the group!
In my area, TWH's (another type of gaited horse) are uncommon, and I was teased for getting one instead of the go-to Quarter Horse. After riding with Sawyer and I, my quarter horse pals were awfully jealous of his smooth gaits and fast but smooth canter.
I personally don't know Paso Fino gaits very well, but I'm sure some people in the Gaited Horse section of the forums may also be able to give you info on events your horse is well suited for based on the gaits.
If you would rather go the eventing direction, you can check out the Paso Fino breed registry, they often have information of events that the breed is currently doing. Good luck! Enjoy your special gaited horse :).
"Putting pads on a gaited horse is like putting a mask on a beautiful woman."