I have a pretty good tool selection and am pretty handy. But I will call a pro as well. Where I live in Hawaii it is hard to get a pro or handyman to show up. They often only come to my area one day a week every 2 weeks or month. So self reliance has become a necessity. But I'm not complaining, I have always been a dIYer having been raised that way.
But I think the better question here is not what tools to have but what spare parts and supplies to have on hand. Things like a spare pump (well or catchment) can be critical whereas, here, the house is always open so sleeping outside under a tarp is no big deal and access to water isn't either. Nor is temperature in Hawaii.
I'm also half hour from an Ace hardware and an hour from Home Depot/Lowes so having supplies on hand is a bigger deal that tools.
My list for real emergencies is stuff to stay clean, fed, and sleep well.
- We have 20000 gal water tank and can gravity draw and iodine sterilize for months. Also keep a stash of bottled water
- Camp stove and plenty butane cartridges to cook and heat water for bathing.
- Lots of cookable food, not preppers, just the normal supply
- Tarps, tent, rolls of plastic sheeting, etc. for shelter
- Gasoline for cars and equipment. I keep about 25 gals on hand but it can get stale so this is based on how much I cycle through in mower and chainsaw, etc.
- Spare catchment pump
- Spare catchment pump pressure switch
For the less major emergencies I keep
- Things to fix plumbing. First choice is shut off water to the problem area and call a pro but I keep things for a self fix.
- Rooter to clear drains (have not used in over 10 years)
- tarps to cover roof leak
- ropes, cording, paracord, and zip ties to secure things as needed
- duct tape
- pipe clamps
- silicone sheeting
- batteries
I have a lot more crap I have around but this is what I can think of would be most useful.