Would it be possible to build a 300 CAD pc that can feel fast? Doesnt need to run any games, just everyday computer tasks, movies etc

Yes

What do you think of this ?

http://ca.pcpartpicker.com/p/vMhjYJ / http://ca.pcpartpicker.com/p/vMhjYJ/by_merchant/

CPU: http://ca.pcpartpicker.com/part/amd-cpu-fd6300wmhkbox ($128.98 @ DirectCanada)
Motherboard: http://ca.pcpartpicker.com/part/gigabyte-motherboard-ga78lmtusb3 ($58.98 @ Newegg Canada)
Memory: http://ca.pcpartpicker.com/part/gskill-memory-f312800cl9d8gbxl ($43.98 @ DirectCanada)
Storage: http://ca.pcpartpicker.com/part/western-digital-internal-hard-drive-wd10ezex ($64.35 @ Vuugo)
Case: http://ca.pcpartpicker.com/part/zodiac-case-ariesa100 ($13.10 @ DirectCanada)
Power Supply: http://ca.pcpartpicker.com/part/evga-power-supply-100n10400l1 ($33.53 @ Amazon Canada)
Total: $342.92
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2016-04-22 00:54 EDT-0400

If you can do it yourself, do you have any parts for a pc already? Case, Monitor, peripherals things like that.

I have nothing, will plug it to my tv and get a cheap keyboard/mouse

What you need is to get a job.