Loads of great advice given above.
Unusual for anyone to get their set up perfect from day one, and am sure the OP will go through a variety of options before figuring out what works for them (we're all different and there's never going to be one solution that fits). However, for what it's worth, after 8 odd years of doing 4-5,000 miles a year of London commuting (plus lots of other cycling), on my preference list would be:
- Gravel or CX type drop bar bike - robust, quick but gives lots of options around tyre choice / clearance, racks etc
- Hydraulic disc brakes - far better all round than calipers and don't bother with mechanical discs - just too much faff to look after by comparison
- 28mm tyres - best compromise of speed / comfort
- Full mudguards
- Ensure bike has rack mounting points to give you options - you may never use (rucksac / other) but better to have than not
- Look at 1x set ups - London is fairly flat so you won't need loads of gears, and no front derailleur means once less thing to maintain / go wrong - I've got this set up on mine and it doubles as my winter bike and can handle all the Surrey Hills, so gearing really is no issue
- Leave as much kit / locks etc at work as you can, and just take in clean stuff once or twice a week in bulk - means you get most of your commuting on a "light" bike
- Defo carry CO2, one spare tube plus Park self adhesive patches. Small pump also in case the CO2 fails (it happens) or you have more than one puncture
Am sure there's lots else.
Most importantly, just get on and try it. Best way to learn and you'll figure out for yourself what really works / doesn't for you, and what's really important.