Staircase refurbishment

I am refurbishing an 1830's terrace with original staircase that has seen much better days from a cosmetic point of view. It is covered in i presume lead based paint that i aint going to scrape off but it is structurally sound and so i am reluctant to get rid of it. Also with it being a in an L shape the quotes to replace are between 1500 and 2000. Plus it is made from 1.75 inch wood that you don't get today.
What i am thinking of doing is somehow recovering it. The underneath was plaster and lath so should i just plasterboard and plaster or should i use wood sheets and which type. Also i am going to put a computer desk under the stairs so could i sink some lighs into it or would this cause a fire hazard because they get hot.
I then need to recover the exposed side and two insides with some nice wood that can be painted but what type of wood would you recommend. I would then fit a new banister and spindles.
I know the above may sound a bit daft (or obvious) but i would welcome any input from more experienced people,

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