What product should I use on new timber staircase?

Hello.There are two things you can do to your stairs:1. you can varnish it.A varnish is a thin layer of protective material that sits over the timber.  It can be water or oil based and clear or with some colouration. I would recommend the Polyurethane Varnish- it is available in both water- and oil-based options, and comes in varieties from satin to glossy. The easiest to use is a clear polyurethane water based varnish.  This is applied with a brush;   you have to work quickly as it does dry rapidly and if you start to brush back into an area that is drying you will get unsightly brush-marks.    It dries to a hard durable finish and a second coat can generally be applied within 1-2 hours Oil based polyurethane varnishes produce an even tougher more durable finish than the water based varnishes.  However you need to apply it in a well ventilated space some people find the fumes extremely unpleasant. It takes a lot longer to dry than the water based products allowing areas to be reworked.  Cleaning up afterwards requires the use of white spirits (even more fumes) Oil based varnishes will colour the wood to a degree so a test is very important.All you need to do is sand down your staicase,dust it up,clean it good and apply the varnish.You don't need to sand between coats. 2. You can also use hard wax oils.They have the advantage that once applied that’s it. You do not have to varnish them (you can if you want to ) Repairs are also easy all that is required is to sand the area that requires attention and apply some more hard wax oil until the area matches its surrounds. Good ventilation is needed as it is an oil based product but it dries quickly and a second coat can usually be applied after 4 – 6 hours. Once sanded and cleaned you can apply the product.No need of sanding between coats unless you need to repair some area.

Very good advice I would also consider using osmo which is available at most paint suppliers now. It was mainly used commercial but widely available after its impressive hardwearing properties. Mainly used on woodwork in bars hotels etc. Hope this helps further.