do I need reverse proxy or forward proxy?
forward proxy, look at this squid guide
I do not have SSH enabled, is it required?
nope, its for managment, to make changes
Could I use lightppd to achieve this?
dunno
What is the best way to secure this proxy connection?
Setup a VPN like wireguard-easy, so that you are not connecting to your forward proxy through open port to the world, but first through VPN and only then to the proxy.
I want to avoid installing 3rd party apps, but I am happy for inightful posts should these be beneficial
Your browser should have proxy settings, so not 3rd party app needed, though some browser extensions like foxyproxy are nice