Red Deal is a softwood and is commonly known as pine to some people - "Pine" covers a large number of woods in the Deal Species.
The older it gets & the more light it gets lovely tones of red and yellows come through. I have a Red Deal Stairs in my house (in fact everything internal in wood is Red Deal in my house except sittingroom floor which is Pitch Pine) all which is clear varnished (Diamond Coat to Floors, Stairs & Door Saddles). As it is a softwood it tends to get marked quiet easily, but as you said you plan to run a strip carpet up the centre.
If you are painting your stairs i.e. white a white deal stairs or white deal stairs (strings) with MDF threads (steps) would be just as good & cheaper.