Most locations
Marriott - Premium brands include W, Marriott, Sheraton, Westin, Renaissance, Courtyard, Méridien. Affordable brands include Four Points, Aloft, Fairfield, Moxy. Luxury tier brands like Ritz, Regis, JW haven’t yet arrived in Taiwan, we only have W. Has hotels even in eastern Taiwan in pretty much every city. ~3k TWD / night for the cheapest option (Moxy, Taichung). Many locations in other places like China, HK, Singapore, and rest of Asia - you can count on finding a Marriott brand in almost every city.
Most affordable options
IHG - They’re known for their extra affordable options (Holiday inn express) as well as luxury brands such as Intercontinental and Indigo. They seem to dominate some southern Taiwan cities so perhaps they have plans to expand more in Taiwan. For example Chiayi has Indigo (luxury), VOCO (upcoming luxury), Holiday Inn (affordable), and no other international hotel brands I’m aware of. Holiday inn express is clean and affordable, probably the most affordable international branded hotel you can find in Taiwan, and 2nd most locations after Marriott. Good number of locations throughout Taiwan in large cities, but no coverage on eastern Taiwan. ~1200 NTD / night for the cheapest option (Holiday inn express, Taichung).
Customer experience
Hyatt - They’re known as the best hotel for giving upgrades if you have status. You have to really beg for upgrades at the other brands due to their franchise model. Unfortunately very few locations in Taiwan and they’re all quite pricey. ~3k TWD / night for the cheapest option (EPISODE, Hsinchu).
Other mentions
Hilton - Currently only 4 locations in Taiwan. ~4k TWD / night for the cheapest option (Hilton, Taipei).
Accor - Currently only 2 locations in Taiwan. ~4500 TWD / night for the cheapest option (Novotel, Taoyuan). Not sure if you count Ibis in this group, as they generally don’t qualify for nights/status and I don’t see them show up in the Accor app for Taiwan.