1. Parameter cheat sheet:

wider, more distorted ← focal length → narrower ("zoomed"), straighter
darker, less grainy ← ISO (sensitivity) → brighter, more grainy
darker ← EV (affects values below *) → brighter
brighter, prone to blur ← shutter speed ** → darker, less shaky
darker, sharp everywhere ← aperture size → brighter, blurs background etc

* - PASM modes mean you control nothing (P), Aperture/Shutter speed, or everything (M), while EV controls all else.

** - Shutter speed (S) can be also conceptualized as the inversion of exposure time (Tv), i. e. shorter = faster = darker & steady, longer = slower = brighter & shaky.

2. Where to learn:

-reading: "Light - Science and Magic: An Introduction (...)" by Hunter, Biver, Fuqua; pretty much all photography books by Tom Ang, Michael Langford and Richard Schneider; the Pics of Asia website; the Strobist blog
-YouTube: Pat Kay, Wolf Amri, Nigel Danson, John Gress, Joanna Kustra, some Anita Sadowska for hands-on look at portrait photoshoots, Now You See It (technically mostly about cinematography, but a lot of the tips also apply to photography)

3. Personal gear recommendations for sub-$500-ish budget:

-Canon EOS 750D (has swivel screen) or Nikon D3300 (very slightly better image quality and 1080p@60fps video; tends to be a bit cheaper)
-18-55mm kit zoom lens
-50mm f/1.8 prime lens (Yongnuo for Canon, Nikkor for Nikon)
-At least UHS-I name-brand memory card (64GB works fine for me, though a larger one would be certainly better for HD video)
-Godox TT685 flash (or Pentax AF200/Yongnuo YN460 if you're on a budget and don't fear manual)
-Some 120cm+ tripod
-Softbox? Waterproof case? Spare batteries? Reflector board? Polarizing filter?

3b. Bonus: gear recommendations if you don't want to carry a heavy bag:

-The original Sony RX100 (truly small) or Samsung NX3000 (bigger sensor and theoretically interchangeable lenses)
-20-50mm kit zoom lens + stock external flash if going with Samsung
-Same memory card as above (name-brand, UHS-I 64GB or faster/larger)
-Mini tripod?