How to ground my PC case and myself? (UK)?

So I'll be building my first PC this week and as it is quite an expensive build, I'm taking no chances and have purchased an anti static wristband to prevent ESD and ease my slight paranoia.

So far, I understand that I should first install the power supply (PSU) in the PC case. I should then, plug it in with the PSU switched OFF.

More specifically, MY QUESTION IS: What do I do with the mains (or wall) socket that the PSU is plugged into? Should it be ON or OFF? Does this matter?

P.S. Just to be clear with the rest of the procedure: from here, I attach the crocodile clip of the anti static wristband to a screw that connects the PC case and PSU. And finally, I wear the wristband.

So I'll be building my first PC this week and as it is quite an expensive build, I'm taking no chances and have purchased an anti static wristband to prevent ESD and ease my slight paranoia.

So far, I understand that I should first install the power supply (PSU) in the PC case. I should then, plug it in with the PSU switched OFF.

More specifically, MY QUESTION IS: What do I do with the mains (or wall) socket that the PSU is plugged into? Should it be ON or OFF? Does this matter?

P.S. Just to be clear with the rest of the procedure: from here, I attach the crocodile clip of the anti static wristband to a screw that connects the PC case and PSU. And finally, I wear the wristband.

Thank you in advance for the clarity! As a former quality and reliability and component engineer at IBM and Lenovo, your risks of damage are higher in dropping parts or getting them dirty with fingerprints that are conductive. ESD is not as serious, and it is mostly about getting the CPU and ram into their sockets and mounting the motherboard onto its standoffs.

Your biggest issues overall come from choice of parts, such as knowing a power supply only by stated watts instead of selecting by brand and model number and a case with good air flow and bottom mount psu face down and computer then on a hard surface.
psu review database: http://www.realhardtechx.com/index_archivos/Page2293.htm

If you have the time, watch a build from Carey Holzman. He is among the best.
https://www.youtube.com/...1UV8jCvIHA

The idea is that you and the parts and the case need to be at the same electrical potential.
If you ever walked across carpet while wearing socks and touch a metal door, you see the spark that damages parts. It generally takes that much. Work on a large flat surface preferably in a room without carpet.
Yes, assuming your house/apartment has grounded outlets, putting in the power supply first and keeping it switched off should connect the case to ground and even touching bare metal on the case once is generally enough. The wrist strap makes the connection continuous.

The risk of issues in this is very low. I actually believe that having clean dry hands and not dripping perspiration on the motherboard is more important. The workers in China wear cotton gloves. Try to hold things carefully by edges and just don't be nervous about it. Place things in general instead of dropping them.
If you perspire a lot, maybe wear a head band. Most of the parts are fairly robust against electrical, but not very good against salty sweat. Honestly, that is the greater concern.
Watch how the CPU is installed, and if using a good CPU cooler instead of the provided one, watch how the prepasting is carefully cleaned and new thermal paste applied. These are the things that get you in trouble, as bending CPU pins or getting "muck" into the pin area of the cpu or holding RAM cards by their gold pins instead of by their side and top edging.

You already describe best practice ESD and that is below importance of keeping clean and dry. All power shpold be off. If your wall socket has a ground pin position, then that is always connected to ground even if the power to that wall socket is switched off. The switch cuts only the hot lead.
A water pipe in the wall is another good ground position.

All power shpold be off.

If your wall socket has a ground pin position, then that is always connected to ground even if the power to that wall socket is switched off. The switch cuts only the hot lead.
A water pipe in the wall is another good ground position.