Is there a command to install basic applications on Ubuntu 16.04?

The fastest solution to install these would be to install the ubuntu-server packageset which has dependencies on these tools and scripts by default. Then you can script the removal of tools you don't need.

However, if you do so, ubuntu-server gets removed (it's a metapackage, it won't break your system if it's removed), and then if you ever run apt autoremove at any point after, those tools will have a chance to be removed since their only dependency point on-system was ubuntu-server

Is creating a script to grab what you want beyond you?

You should only grab the bare minimum set of tools you need, so it's better to create your own minimal set than use a predefined set created by someone else (it'll likely contain packages you don't need)

As @Rinzwind said in comments, your script may also include the removal of default installed packages you don't need (ie. to help achieve the minimal packages your system actually needs).