For the accommodation booking, I mostly use Hotels Combined One thing I recognised lately that in many cases the price of the hotel shown on their website is not the final one. Taxes were not added. Check carefully.
I check the review and pictures of the accommodation on the Tripadvisor I pay a special attention to the noise level, location and tiredness issues of the property.
For Asia it is worth additionally look at Agoda This website like the Booking as well has the insider deals for registered customers. Those you can’t find using Hotels Combined only.
For searching the flights I use Matrix Airfare Search You can’t purchase the flights there, but have the overview of the possible options. Upgraded Points have a detailed instruction of best use of Matrix. For the actual booking of the long haul flights I mostly use Expedia In some cases I also use Google Flight Search
I use travel agencies very rare. Still I would like to recommend the travel agency of Turkey Backpackers Travel I used their services for my Cappadocia trip from Istanbul.