The head is very unlikely to need skimming. It will probably just need cleaning and rubbing back with a sheet of emory cloth on a flat block about 3" x 5". Heads almost never warp. In fact I've not seen a warped A-series head in over 55 years of working on them. The block never warps. The only issue requiring skimming is when water erosion has happened and this is obvious when you emory block it down.
You will need a new head gasket and you need to check the valves and valve seats. Re-lap the valves if the seats are pitted, but if they are burnt you will need new valves and re-cut seats - a job for the machine shop.
Rather than pay someone to change the head gasket you will be better doing it yourself and spending the money on tools which you will need in the future. As a new classic Mini owner the sooner you get into DIY-mode, with the help of us on here, the better for your wallet .