You have a handful of ways to try out LXDE.
But I am totally new to those Linux things
We encourage you to try out Lubuntu, which is based on Ubuntu Linux, and made by our community members.
I have a Linux or BSD running on my computer, and I want to try LXDE
Sure. You can install LXDE easily. Please follow the wiki page to find out how to install LXDE for your distribution.
I want to buy a low-budget computer with LXDE
If you want to buy a computer, you can consider getting a single-board computer for a fraction of the price. Many single-board computers preloaded LXDE as their default desktop environment.
You could also consider getting a computer from a local computer recyclers and ask them to install Lubuntu on it.
Although it could run on the computers with RAM as small as 256MiB, We recommend getting a computer with RAM of 1GiB or above for applications running on it, such as web browser, video player and office suite.
I would like to get the source code
If you are looking for the source code, we are hosting them in the SourceForge projects: