Let's break down this question in parts and start with the FOSS licenses common ground.
The common things about FOSS licenses are that
- one is required to keep the copyright notices of previous authors.
- one must not misrepresent another person's work as yours and vice versa
(which in essence combines to being honest of who did what).
The GPL as a strong copyleft license goes a step further and additionally requires that
- any work which makes use of it is also required to distribute the source under the same conditions (and no additonal restrictions!)
Now to the first question, including GPL - licensed components and adding additional restrictions: No, that does not fly. You cannot require active code or advertisement in any specific form. You can only require the proper attribution, and you must keep the conditions on distribution without making them stricter. The GPL FAQ has a few answers on various restriction scenarios.
This might be different, if you include a "library" under the LGPL; in that case you might still be allowed to choose whatever license you fancy provided you allow users to replace the library by whatever they want.
The more permissive licenses have no such restrictions either - they only require proper attribution and allow you to distribute your code even under proprietary licenses (including no distribution).
There cannot be any FOSS license with a restriction of required advertisement like you suggest as it fails the desert island test: such software would not work in an environment where links don't work.
All this said, I'd still recommend to use the GPL. Add an appropriate copyright notice to your files like
(c) 2022 Porton from http://my-fancy-software.example.com/
and if you feel like add these links where you consider them appropriate. Also add in the readme a kind request like
If you like this software and want to help its continued development, please support us by keeping the links to our software or linking us in this form: (add the code snippet)