If you can use a transformer closer to your target voltage, all the better. A volt or two extra is nice to allow the regulator to regulate when the line voltage isn't quite perfect. However, many transformers are rated at high load (for their target capacity) so light loads will be higher still. Furthermore, RMS AC rectified to DC will result in a slightly higher DC voltage.
Aiming for a 6v AC transformer will give you some cushion if you use a 5v regulator. If you go higher, then using a 9v regulator will shed some of the excess as heat, and then your Nano's onboard regulator will shed the excess from 9v to 5v as heat. This is better for each of the regulators than going straight from (say) 12v to 5v, as the waste is dissipated via two regulators instead of one.
Re: fuses. I would always, always
put a fuse on any mains-connected PCB. Just in case. There is all manner of excrement that can occur. Sure, your UK power cord may have a 3A or 5A fuse in it. But if you have (for e.g.) a transformer rated for 250mA, how's it going to feel about passing 3A until the fuse blows? Circuit breakers and even power cord fuses are rated high enough to not trip as a nuisance. A product's own fuse is rated for the expected load of the product, and will tend to be a much lower value. I don't know what the laws are, or even what common practice dictates, but if it were me, I'd pony up that $1 or so for a 250mA fuse. It's cheap peace of mind. Your house, your life, so it's entirely up to you, and I won't arm-wrestle anyone that wants to do otherwise. It's just my not-so-humble opinion.