Honestly I don't see the editing you want to get done working to well for that price since you are talking about Canada prices which are already higher than U.S. prices, and then the costs of the monitor, keyboard, and mouse will take up $150 of the budget right there. I don't think that $500 will get a sufficiently decent editing computer.
Avid system requirements are at:
http://www.avid.com/US/products/media-composer/specifications
You can see the minimum system requirements vary depending on what you are wanting to do, but can go up to 8 GB minimum required RAM...and recommended 16 GB for other functions. The GPU minimum requirements is not very high and on die GPU would work for it...not the best...but would work.
The minimum CPU that they want you to have is a quad core i7 or quad core Xeon...which starts in the $200+ range.
I don't know which specific Adobe programs you are referring to, but it seems if you can run Avid, chances are you can run the Adobe programs...unless of course they are more GPU based...so I could not say for sure about that without further clarification.
So, what specific Adobe programs are you talking about running?
With all of that being said, I can't really recommend anything. I would estimate the costs would end up being:
CPU $200 - $250
PSU $25 - $40
GPU $50 - $100 May end up being optional depending on integrated CPU graphics and specific Adobe program system requirements
RAM $75 - 150 Depending on specific functions of Avid you plan on using
Optical Drive $15
HDD $50
Case $30 - $50
Keyboard/Mouse $20- $30 for cheap ones
Monitor $100 - $150 Depending on specifications
Motherboard $30 - $75 Depending on specifications
So while it is possible to do, depending on what you really need to do with the programs and if particular parts are needed...those prices are in U.S. dollars and I am sure that there will end up being a higher price for purchase in your region.
I wish I could be of more help, but I will continue to monitor this thread and try and assist after your response and others have posted.