To type in IPA, switch to an IPA keyboard layout. It is much faster than hunting through the Character Map. I use SIL's keyboard software, available for Windows, Mac and Linux.
For Ubuntu instructions, see How to configure keyboard to type in IPA fonts?.
Edit by OP:
Here is how to set up IPA Keyboard for Ubuntu 16.04:
Download the SIL package as a .deb file from packages.sil.org & install with GDebi or
sudo dpkg -i sil-repository.deb
sudo apt install ibus-kmfl
sudo apt install kmfl-keyboard-ipa
I got the right keyboard package by guessing the name, as I couldn't find a reference list anywhere on the SIL pages
Then in Settings > Keyboard > Text Entry
Under Input Sources click the + button to add a source and search for 'ipa', and it should come up. Click to add it.
Switch between input sources with Super+Space (this can be changed in Keyboard Settings)
You will need this chart to figure out how to actually enter the IPA characters!