I'll go through your Q point by point.
Do I need (hdmi to vga adapter) OR (vga to hdmi adapter)? My common sense would tell (vga to hdmi adapter), but I am not 100% sure.
Well, the exact naming of the adapter will depend on the vendor, but most vendors put the video source (computer) before the "to", and the video target (monitor) behind it. So "HDMI to VGA" would be an adapter for connecting an HDMI output to an VGA input, which is what you need. But the naming convention is not universal.
Note that HDMI-VGA adapters usually only work in one direction - so check the description for the adapter before buying, so you get the right adapter.
I have seen some people in online forums talking about active and passive connector. It is turning me crazy. I can't really grasp that. Can you tell me like a layman, what should I be using?
A "passive connector" is a connector that does not "do" anything - which means it does not have electronics inside that convert the signal. Instead it only electrically connects different plugs. That only works if the required signal itself is the same on both sides (or compatible). So passive connectors only work in certain situations. For example, you can go from DisplayPort to HDMI with a passive adapter (because DisplayPort was designed that way).
HDMI and VGA use completely different signals, so you need an "active connector" (or "active adapter"), which contains electronics that will convert the signal.
Further reading: How to convert HDMI to VGA or VGA to HDMI . This article gives more explanation about the technology required.
Wikipedia also has a section on HDMI to VGA conversion: HDMI - Legacy compatibility