Do the Models Matter (Waffen SS vs Heer Vs Fallscrimjagers VS Winter Heer etc?)

Hi,

Sorry total noob question here, but are there any actual in game differences between the type of model are are they all just 'infantry' or 'veteran infantry'?

I have the BoB starter set on the way (Grenadiers) which his a late war set but I am also looking at the various Starter Armies.

The Waffen SS army looks good but it is obviously .... controversial.

The backup option would be the Grenadiers army.

I was thinking of buying that set but just painting the infantry in a normal colour to blend with the grenadiers.

I like the idea of a German army which can be played in as many theatres / settings as possible without being too anachronous.

I also have a sprue of winter fallscrimjagers (6 men) from a magazine freebie. Do paratroopers exist as a separate unit or could I just run these alongside the Grenadiers/SS models?