I use Google hotel search as a first point of call. Usually traveluro or it's sister's sites come cheaper but occasionally also trip.com or Agoda. I've booked with all of them in the past, so far so good but I understand the concerns about dodgy booking platforms. Sometimes even the hotel's own site comes cheaper on Google. Both trip.com and Agoda give extra discount on their apps.
Needless to say , you won't get status perks on hotel chains if you don't book directly.