What should I carry around with me

[Apollonius]

Totally agree with the travelling light idea. Not much point in buying a light bike and then weighing it down with stuff you "might" need. On the other hand, there is stuff you WILL need, and that means puncture repair stuff. If anything else goes wrong then that is mostly down to poor maintenance or not setting the bike up right in the first place. And the key to proper maintenance is cleaning.
I carry everything I need in a Vittoria bottle-cage tool-case. Mini-pump, CO2 pump, Park Tools self-adhesive patches. New tube. Two plastic levers. Quick link. . Phone in plastic bag in jersey pocket and a £20 note for food and beer.

 

[vickster]

The OP bought a mountain bike

I don't tend to travel light either if on the Genesis anyhow

I can't bear having anything other than mitts or a gilet next to my lower back so jersey pockets are barely used (big scar from back surgery 20+ years ago)

 

[Profpointy]

For a long ride, pump, tyre levers, spare inner tube (or 2), patches, multi tool or allen keys, spanner (if there are big nuts), or maybe pliers if just small nuts. Maybe / maybe not chain tool. Electrical tape and cable ties for bodgery, phone and cake money.
Water & (maybe) food - though money can suffice for the latter - route depending

I never carry first aid kit. If you can self treat and ride on then you can man tf up and do without, and if you are proper injured I doubt you're going to carry a leg splint after alll

 

[palinurus]

A hip flask, a bugle and a pistol.