Yes, benchmarking can work.
Better hosting will cope better with heavier, more trafficked websites, so it's only really a start.
How hosting copes with multiple active visitors, a number of plugins, and often unoptimised themes and images can vary greatly - the storage, web server, and how crowded the server is will make a big difference with that.
Pure SSD storage is much better for reliability and performance, so you can look for a host that provides only that.
LiteSpeed web server or Nginx will also perform better than standard Apache which many web hosts run.
LiteSpeed provides LiteSpeed Cache for WordPress:
https://en-gb.wordpress.org/plugins/litespeed-cache/
https://www.litespeedtech.com/products/cache-plugins/wordpress-acceleration
This works directly with the LiteSpeed web server for the best caching performance, and can make a real difference.
Finally the number of users on the server makes a big difference, and you can test this through benchmarking and simply using the control panel and backend. This will be slow with the large commercial hosts, that cram far too many users onto ageing servers.
This is a popular tool:
https://tools.pingdom.com/
We routinely run that after migrating clients from the likes of Vidahost to see the speed improvement.
You can also check reviews and feedback from other users. If you do a search on the forum you should find plenty of recommendations, hopefully including us.
If you have any questions feel free to get in touch.
All the best,
Dan