Here are several steps that admins can take before agreeing to install user-requested applications. A good goal would be to have the users do these things before coming to you...

$ apt-cache search thetoolname will give you a list of related tools, that can be checked for the best fit.

$ apt-cache show thetoolname will give you a blurb about what this particular tool/app is for.

Check the application on Debian's popcon ("popularity contest") to compare how many reported installations there are of the requested tool.

https://popcon.debian.org/

or

https://qa.debian.org/popcon.php?package=thetoolname to directly search for your tool.

For example, for htop (which is a nice, clean-looking, command-line process viewer) popcon yields:

... along with the corresponding maintainer's page:
https://qa.debian.org/developer.php?package=htop

When installing -- always check over the dependencies. See if they would bring in something you may not want.

debsums is another tool for verification of installed package files against MD5 checksums

$ debsums -l *or* --list-missing # list packages which don't have an md5sums file. (It should really come back with nothing.)

$ debsums -c

All of this helps to give you a feel of the general acceptance of the tool in question.

One additional place to ask questions about packages is on the #debian user's email list.

Subscribe by sending an email to:
debian-user-REQUEST@lists.debian.org
with a subject of:
Subject: subscribe your@email.com

You can find past mailing list threads here:
https://lists.debian.org/debian-user/

And other #debian mailing lists here:
https://lists.debian.org/users.html