At the moment, I'd probably be reluctant to go much more than 10 miles from home (10 miles being the distance I'd be OK with walking if the bike couldn't be ridden). I do take spare tubes with me, and I am happy changing a tube, but I haven't got the strength to get more than about 60psi in the tyre without a track pump, so it would be a very careful ride home.
I'm not prepared for things like a broken chain or snapped cables, so I need to think about those things before I go further, I think.
I can't get more than 50psi in a tyre with a mini-pump, it will do as a get home measure though.
For a broken chain, get a chain splitting tool and a powerlink.
You can still ride a bike with a snapped cable, if it is the rear derailleur cable then it means you will be stuck in top gear. If that is a problem, you can adjust the high limit screw to bring the derailleur in line with a larger sprocket.
Worst incident I have had was when my chain overshifted, got snagged then yanked the rear derailleur so violently it snapped, went through the spoke guard and buckled two spokes, destroyed the cable, twisted the chain through 90 degrees (thus destroying the chain) and tangled the chain up so badly it locked the rear wheel. Fortunately I was only 1 km from home when this happened.