There are several reasons to use travel apps- buy an airline ticket, book a hotel or rent a car.
On top of my list here are Travelocity and Kayak. They are both reliable and easy to use. Lately I use Kayak more- it looks that the search results are better and I am able easier to define the criteria.
It could be a good idea to download the app of the airline that you are using. Some of them will give you flight information and the opportunity for on-line check-in. I used many times the Lufthansa app and it works very well. Other apps that I can recommend are the ones of Austrian airlines, British Airways, United Airlines, KLM, jetBlue.
Book a hotel/apartment
Here the choice is between Booking and Airbnb. Both are fine- you can use the first one for hotels and the second one for private rooms/flats/houses. Another opportunity for hotels is Trivago that compares many different offers.
Rent a car
If you want to bypass the taxi service you can use Uber. The problem is that there are number of countries which have not allowed the company to operate due to regulatory requirements. Still if you prefer to be the driver of your rented car my proposal would be to use Budget (1st choice) or Hertz (2nd choice).