There are plenty of "right" ways of doing this, Sahida. Everyone will have their own preference.
Dulux Diamond is one of the best. Water-based is often preferred by many decorators.
Apply "knotting" solution to any knots first.
Then one slightly thinned coat of water-based primer.
Then 2 coats of Diamond.
For the treads, I would use a hard-wearing floor lacquer such as this........
http://www.decoratingdirect.co.uk/viewprod/j/JUNSTG/
There are plenty of other floor lacquers if you can't get this one locally.
I often use it for wooden kitchen worktops. It's virtually bomb-proof. Stairs take a lot of hard use.
If you want Walnut, then simply colour the treads with "Colron" wood dye first.