Mudguards - No immediate plans to cycle in muddy areas, or on wet days. But will keep in mind.
Rack
Pump - Yep
Spare inner tube and repair kit.
Lock - Self explanatory - also needs to be silver rated for specialist insurance.
Lights - No immediate plans to cycle on evenings, but will keep in mind in medium term, I.e few months down the road towards winter if we have a nice winter lol.
Helmet - Self explanatory that one
Mitts - as above
Trying to start with the basics, bike, lock, helmet.
If I enjoy it a lot, then I’ll start looking into winter / bad weather accessories and then probs towards next summer get things like bike racks as I know they are one of the more expensive addons.
If you want to restyle your physique you will need to ride all year round, which is easy to do in the UK, baring a week or two of icy weather and the occasional storm.
Mudguards are for wet roads which are far more commonly encountered than rain. Water on the road is dirty and leaves a trail of dirt on your clothes. It forces you to wear a waterproof when it is not raining.
Mudguards let you ride in dry confort, wearing a windproof top, on cold damp days with wet roads. Riding without 'guards in winter is just making life hard for yourself.
Some companies make mudguards that can be clipped on or held with rubber bands but those are both hack solutions for when you can't fit SKS Chromoplastic bolt-on guards. If you buy a bike that can fit bolt-on guards, you have option to fit anytime later.
Same with rear luggage rack , you dont have to fit them and many people dont. Should you get the urge to go bicycle touring, you just bolt a standard rack to your standard rack eyelets and you have expanded your cycling capabilities hugely. Without the eyelets you are reduced to hack solutions.