We're in and out of FCO at least once a year, and I think it is totally fine, and I would not say anyone should avoid it. It is not too big, the signage is good, and transport into Rome is (reasonably) straightforward.
Taxis have fixed prices into the centre, probably €60.00 now. There is a different stand for taxis into the city, vs taxis to other places: there are staff to guide you. There are also busses and we've used that system once. Access to the train is from the upper level and through the tubular overhead walks.
There are two train options. The Leonardo Express is direct to Termini, with no stops. It costs probably €14 and departs every half hour or so; we haven't used it for a few years so those details may be out of date. It is clean and fast. The regular train is about €8.00 and leaves every 10 or 15 minutes. There are ticket windows and machines, and there are english-speaking staff at the gates to guide you the correct train. These trains stop at many places along the way so if your destination is not at or near Termini, it may be a better option. Do check for strikes as .... they happen.