First let’s talk about “Old Engine”
Old Engine refers to builds of the Source Engine before the Orange Box release, so for example Source Engine branches such as Source Engine 2004, 2006, etc… Old Engine has a lot more glitches than the version most people run today and is almost completely different.
New Engine refers to builds of the Source Engine after the Orange Box release, so for example Source Engine 2007, 2009, etc… New Engine is the version of the Source Engine most people run. It includes ABH and other neat tricks you might’ve seen from Half-Life 2 runs over the years.
Now let’s talk about “Source Unpack”
Source Unpack is a package that contains a New Engine version of Half-Life 2 that most people have been running over the years. This is a clean version that was officially released by Valve without any modifications.
Ghosting mod is a mod for Half-Life 2 that is geared more towards speedrunning. This is the thing most who run HL2 uses. It includes features like recording ghosts, a timer (although outlawed) and a speedometer.
If whenever you come across a Half-Life 2 run with a timer, just note that that timer is most likely LiveSplit, the timing program for most speedruns. When you run Half-Life 2 it is a requirement that show LiveSplit in the recording; most people do it using their recording software.
Now that we have clarified with terminology, I believe you are wondering should you run New Engine or Old Engine. New Engine is very easy to get into nowadays, the movement is fast and forgiving and the tricks are, also. Most of the skips in Old Engine involved very complicated Save Warps and Triggerdelays which are very hard for a beginner to get into.
So in short, you should run New Engine.