Yeah sash colours were primarily red for the Royalists, although the tone appears to be more a pinky rose colour in most paintings of the time:
Orange was Essex's Colour, the Southern Association wore Yellow sashes since that was Waller's colour and the Northern wore blue since that was the Fairfax's. The Eastern Association may have worn green sashes, Manchester's colour. The New Model switched to the Fairfax's blue when they were formed and then, surprisingly, went to red later on. A few individual officers would also wear whatever sash they wanted, Cromwell wore a white sash for example.
Orange is probably best for Parliament if you want just the one sash colour. There is some debate on the exact tone of orange (tawney, a more browny orange colour has also been suggested) but I think it would vary from soldier to soldier so as long as it is recognisably orange you should be fine.
To be honest, the soldiers would barely have been different in appearance, if anything the Royalists had a lot less resources than Parliament (hence why Parliament did, albeit briefly, have one full regiment of cuirassiers). That said, the montero was very popular with the King's Army, which is a bit fancier than the average hat. Drummers would be very well attired.
With the cavalry, the King's Lifeguard would have been pretty well equipped with the usual lobster pots I would imagine , being the personal troops protecting the Monarch, they have red tunics in some depictions of them so if you had a 'lifeguard' rank for the Royalists you could have them in red tunics with lobsterpots and then 'cavaliers' below that in more fancier civilian gear. Some sacrifices do have to be made in games to allow for a bit of variation, added with the fact that we really have little to no information on uniforms for many regiments. We know buffcoats were popular on both sides but, again, soldiers would have to make do with whatever they could find.