The x ring is 1/2 moa, so ideally you have a weapon and load capable of grouping inside of that, of course the rest is up to you.
F/tr is more regulated in what you can use. F open is more "open," in what you can use. This includes caliber restrictions.
As far as what an fclass rifle is, it is whatever you want it to be, inside the rules of course. Mine is my coyote rig, I use fclass as a way to become more proficient with my gun, as well as a way to enhance my skills as a marksman, just for hunting purposes.
I use a Harris bipod up front, and my hand as a back rest, my weapon is stock, with a skim bedding job being the only smithing done to it. So, I am very basic, I run an 8-32x56 power scope, high magnification is a good thing to have when aiming at such a small center ring. Nightforces 12-42power benchrest scope is popular, though mirage puts a damper on that high power at times.
But, I see a huge variety, from your grandpa's old 700 with his 3-9 power scope, to what appears to be a weapon best suited for the top of a tank, with a front rest needing a masters in engineering to figure out.
The two classes give fclass a "run what you brung," kind of feel, and so you do see that great variety in what people use, but, you don't see the arrogance that could come with using a $3,000 scope, $8,000 complete rifle...