Hey, welcome to RIU
ive been doing alot of research and question asking lately in regards to building new lights. I am far from knowledgeable on the subject, i can however repeat what some very very smart LED guys have told me.
$500usd can def get you the material needed to build a nice light for a 4x4
Im building this light for a 4x4 footprint as well, currently I have 15 x 4` strips and 2 x 320w drivers in my cart and total cost is $370usd. So its def dooable. That would leave you with $130 to get material for frame,wire,wagos etc ( digikey.com is your friend if your going the strip route)
~HLG also sells quantum board kits that are all the rage, not sure what price point is tho
~Alibaba also sells quantum board knock offs that seem to be preforming well, there is a huge Chinese knockoff thread in the LED section full of great information and very helpful bros.
Head over to the LED subsection
https://www.rollitup.org/f/led-and-other-lighting.124/
Also this site is amazing for new to the game light building
http://ledgardener.com/diy-led-strip-build-designs-samsung-bridgelux/
hope this helps, as i said, im just repeating what ive been told or have read over the past month or more since i began down this rabbit hole lol.
Best of luck