I remember getting to Elite on the Amstrad CPC version. Took ages! I had a lot more spare time then.
From memory, to progress faster we used to enter witch-space, destroy the 4 thargoids there, scoop up the tharglets(?), sell them, rinse & repeat.
There was also a cheat that enable you to expand the cargo bay beyond it's normal capacity. I can't quite remember how to do that but I'm pretty sure it was something to do with the tharglet collecting. Very useful.
I think the missions on that version were; destroy the cloaked Asp (which got you the cloaking device), rescue the refugees from the star going nova, and destroy the thargoid base.
Oh yeah, and mining lasers ruled - 4 shots for a thargoid!!
Was very cool, Right on Commander!