Your question should be divided into multiple parts as there is a lot of topics to be covered.
Firstly, as it is the case with everything else, with determination you can learn anything and in this perspective Linux is not different. In my opinion the best way to learn Linux is to simply use it. There is a plethora of resources available free of charge on the net, hundreds of communities and Linux user groups you can visit either personally or online.
Choice of Linux distribution:
There is no bad distribution as the choice is really only a matter of personal taste. Most of the new Linux users choose Ubuntu or Linux Mint as they fell that it is easier to use and more up to date.
For me however, Debian GNU/Linux is also a Linux distribution choice for everything. I run Debian on servers, laptops, gaming desktop, Raspberry Pi etc. Debian has a great documentation a community.
Once you have a Linux desktop installed start to play with it and familiarize yourself with it. Then I would recommend a book “LPIC-1: Linux Professional Institute Certification Study Guide”. This is not the best all-in-one comprehensive guide on how to acquire Linux skills, but it will provide you with a structure and guidance. Combine that with endless on-line resources and you would be good. Note, I’m not suggesting here that you should do LPI certification, I only recommend this book because its Linux distro agnostic ( except few pages about package management ) so it will provide you with a solid Linux background.
Once you are more comfortable with Linux, feel free to move to next step and install your server. Any decent Linux distro will do including Debian. The service installation you are talking about is know in Linux community as LAMP ( Linux, Apache, MySQL, PHP ). It is also possible that you will be able to fit everything on your old laptop. Remember, words like old hardware, do not have the same meaning when it comes to Linux. To install LAMP on debian all you need to do is to run:
# apt-get install libapache2-mod-php5 php5-mysql mysql-server
and you are done. The above will install PHP, Apache Web server and Mysql. When it comes to mail server you have multiple options such as postfix or sendmail just to name a few. But again, take it step by step.
If you need more help, feel free to ask … !