Synthetics usualy more resistant to high temperatures and pressure and therefore lasts longer (or at all) in a modern engine. Mineral or part synthetic breaks down with use, although some cars have it as running in oil for this reason as it allows the moving parts to effectively polish each other when theyre factory fresh and a bit tight. On an old engine anything will probably work, just change it frequently as cheap oil doesnt last and the engine will be filthy so your flushing out that crap.
10W40 means it behaves like 10 weight oil when cold and 40 when hot. That does not mean it gets thicker, but its only as runny as hot 40 weight oil, rather than hot 10 weight oil which would be really runny. So unlike a ‘normal’ oil its viscocity changes relatively little with temperature, which is a good thing.
Old cars might benefit from slightly thicker oil than when new. It helps the pressure remain high and stays put better. It also makes the engine a bit quieter.
I’d just use the right viscocity and type recommended by VW and get whatever is cheap. I usually pick up magnatec or mobil 3000 whenever asda has them on offer for <30quid a gallon.