Hi,
as you said in your project description, it is a simple job, but will take a few days to make it all work properly and to be look-alike to the old website, but with a touch of modern design. In these cases, i prefer using paid themes, like Enfold, which has great support and regular updates, with creation of child theme and base all on Wordpress, which will give you ability to change/add new pages/items/data cause it has awesome page builder from the backend....but i can give you some points how it all work if you need them.
Would like to know how many pages current website has, and would you like to add some new functions to the new website?
Free to answer any Q's you might have
Best regards
Stoyan Vasic
Novi Sad, Serbia