I always get trip insurance for all my big trips (i.e. ski trips and bike tours). If I have one piece of advice, it would be to put on your lawyer hat and read the fine print. Ultimately, if something gets covered or not is spelled out in the coverage definitions. Just about every policy has variations in definitions and exclusions. I personally do not have a single go-to travel insurance company. It really depended on my needs at the time and what I was going to be doing on the trip. One site that I use a lot is squaremouth.com. You can do side-by-side comparisons of policies and have easy access to coverage definitions.
You asked about if you get injured prior to the trip and cannot go on your tour, that would typically fall under “cancel for medical reasons”. You don’t need “cancel for any reason” coverage for that. Usually, “cancel for any reason” is needed for something like if your boss is a big jerk and makes you cancel your vacation. If you get injured on the trip, then that would be considered a “trip interruption”. One thing to watch out for is the timing of purchasing the policy. If you are already nursing an injury before you purchase travel insurance, then that would be considered a pre-existing medical condition, and you would not be able to use that as a covered reason to not go on your trip. Some policies will waive pre-existing medical conditions if you purchase the policy within X days of putting down your first deposit for your trip.
Should something happen and you need your trip insurance policy to kick in, get as much official documentation/receipts as you can, and try to do it promptly. You will not be able to put in a claim without it. It’s a lot harder to get overseas medical records. I personally know someone who thought a bunch of photos of her injury would suffice. No dice.
Now that I’ve spewed out a bunch of nuances about getting/using trip insurance, the companies that I’ve used in the past are (in no particular order….just what is being served up by my memory): Allianz, Travel Insured, Tin Leg, Trawick International, John Hancock.
In terms of bad experiences with insurance companies, most of the times I’ve heard of a denial had to do with the cancel reason not fitting in the definition of a covered reason or due to poor documentation. The one time I personally had to call my travel insurance company was when I broke my collarbone (yup, from a bike crash). I already had purchased the policy for a ski trip later that year, so no issue with pre-existing conditions. Broken collarbone didn’t heal, so that meant having surgery which was scheduled right in the middle of my ski trip. I decided that I wanted to go for the first 3 days of the trip and then come home and have surgery. Unfortunately, my desires and the coverage definitions for my trip insurance did not jive. If I wanted to bag the entire trip, that would have been OK. It would have been considered a medical reason, and I would have gotten a full refund for my trip. I didn’t want that. I wanted an early return home. Well, an early return (a.k.a trip interruption) would have only been covered if it was due to something that happened while on the trip. I did end up going on my abbreviated ski trip, but the trip insurance didn’t help me in that case. It did work out in the end because my flight just happened to be on Southwest which made it really easy to change my return flight at no cost. The resort refunded the unused portion of my lift ticket. The only thing I really lost out on was lodging.
Let me know if you have any other questions.