Well, this changes things a bit.
A dedicated graphics card would speed up graphical processes by a significant amount.
Lets see,
Core i7-6700 - beast.
8GB ram as mentioned - will do fine.
the same 300w power supply
SoniaH H110 motherboard
This motherboard has PCI express x16 lane (written in PC specifications), which means you can get any new graphics card and install it easily (also need to have a powerful enough PSU).
You're right, this PC does not have a graphics card, it uses integrated graphics (intel hd series). Since the power supply unit is only 300w, my recommendation stays the same: Nvidia's GTX 1050 or 1050Ti are the cards that require no additional power connectors - they will draw power from the motherboard (Ti version is 15-20% faster). According to game-debate, 300w PSU should be ok:
http://www.game-debate.com/hardware/?gid=3541&graphics=GeForce%20GTX%201050
http://www.game-debate.com/hardware/?gid=3669&graphics=GeForce%20GTX%201050%20Ti%204GB
Higher-end graphics cards would require a better PSU and if you don't do 4K or higher resolution images or video editing, you should be fine with nvidia's newest generation mid-level graphics card.