Phil - it depends. If your home is new then there is no need to put aside large chunks of change for repair, however if the home has age, then things are bound to need maintenance and repair.
First let's talk insurance, in the US insurance attached to homes seems to come in two forms, first is PMI which is mortgage insurance and is USELESS for anyone other than the lender, it does NOTHING for the purchaser, the other is homeowner's insurance which really only covers the structure and contents from major damage. There is a home warranty which I guess is an insurance of sorts which can be purchased, often it is not worth the money spent.
As far as what to set aside, again, it depends on the age of the home. I'm tapping on 13 years old and had a roof vent leak and two other leaks so my repair costs were about $400 which is really not an amount I need to set aside. My AC units just let me know they were old and the repaid costs were $210 which amounted to refilling with refrigerant, but I now know they are both in need of replacement. To go a fairly energy efficient route will cost me $8K or so. Your roof will last 25 or so years, so in 10 years I need to be prepared for shingles, let's put that at $10K. My water heater is relatively new and should need to be replaced in 15 years or so (tankless) so I need to be ready to take a $2K hit. It all sounds like a ton of money, but with $10K available you can cover most any repair from small to large. Most larger items can be financed if need be so a slush fund of $3K would be adequate IMO.
I can just see the OP crunching numbers, so let's put it in perspective. I purchased the home in 1998 and in 2010 when we refinanced the value was up 40% even in our down housing market.
Growing up we always had a large garden. I'd say ours was at least 1/4 acre, perhaps 1/2 and 5 of us ate a ton of vegetables often giving extra away. I don't know how much it saved my parents, but we were not well off as it turned out. I thought my parents were cheap, turned out we were poor