Question: Does someone knows a small linux distro that comes with apt package?

I tried puppy linux and dsl, but I didn't like any of those.

I am looking to setup a LAMP into a virtual machine with a small linux, and I am looking for a distro with apt because i am familiar with the package, and it would be easier for me to setup and upgrade a server.

Answer: 
Ubuntus JeOS was beeing build for exactly your purpose.

<https://help.ubuntu.com/community/JeOS>

as single iso until 8.04

Now part of the server iso. Just select "install minimal virtual machine" in the install menu.
Well for light DE you could try lubuntu.

If you just want something light, then use the Ubuntu minimal install and build from there