Office work can generally be done on any of the newer hardware so an i5 or i7 would work fantastic for all of that, but if you want to game you will definitely want something with a graphics card in it. Given that you are upgrading from (at this point) a fairly old laptop something with a rtx 4060 or even a 4050 would be worlds better for gaming. For a cpu you could easily downgrade to an i5 and that would be plenty.
So overall I would recommend trying to find something in a similar price class that has an i5 and a rtx 3060, 4050 or 4060. These graphics cards would all play games like the ones you mentioned (skyrim, fallout, and other older titles) at 1080p.
Office work can generally be done on any of the newer hardware so an i5 or i7 would work fantastic for all of that, but if you want to game you will definitely want something with a graphics card in it. Given that you are upgrading from (at this point) a fairly old laptop something with a rtx 4060 or even a 4050 would be worlds better for gaming. For a cpu you could easily downgrade to an i5 and that would be plenty.
So overall I would recommend trying to find something in a similar price class that has an i5 and a rtx 3060, 4050 or 4060. These graphics cards would all play games like the ones you mentioned (skyrim, fallout, and other older titles) at 1080p.