Bottom Line: The narrower you define your focus, the easier it will be to cover your general liability needs.
Detailed Answer & Experience:
There is no set criteria to look for other than "will they cover me?". My initial criteria was speed. I had a huge client that required specific coverage (happened to be a healthcare products company) whose contract I would not win without the coverage. I bit the bullet on cost, and made up for it in revenue.
In my first consulting agency, I couldn't get signed up with Travelers Insurance because I had clients in the entertainment industry (we created a lot of band websites). This was one of their red-flag industries at the time that they simply didn't touch as a matter of policy. The Hartford took us in, but it cost more because they had a bunch of rather ridiculous requirements (terrorism insurance) that weren't relevant (kind of like making a man have maternity coverage)... but ultimately they covered our group.
In my second consultancy, I used Techinsurance as a broker. They have a good understanding and focus on tech firm needs. For me, they were the cheapest and fastest way to acquire general liability insurance. It's niche-specific though.
Healthcare providers are in a completely different ballpark, as is wellness and coaching. Personal trainers can get their own independent insurance through Idea Fitness, ACE, etc. It is, without a doubt, the cheapest way to go for the individual trainer.
Most general liability insurance is tailored to the specialization. I cannot speak for malpractice insurance... but it's definitely crossing into a grey area. Since your needs cover many different specializations, you may need to deal with a broker who explicitly specializes in health provider insurance.
Business structure is definitely something to consider if insurance is going to be a big cost. For example, hiring a personal trainer on a 1099 contract could transfer the "burden" of professional insurance onto the individual. Pay them enough to cover that and make sure they qualify as a contractor in your state(s). I'm not a lawyer, and every state is different... but I do know that approaching an insurance company with a narrower focus and alleviated burden will make it easier to acquire general liability insurance.