Catalyzes the phosphorylation of mevalonate to mevalonate 5-phosphate, a key step in isoprenoid and cholesterol biosynthesis. (R)-mevalonate + ATP = (R)-5-phosphomevalonate + ADP + H(+) Farnesyl pyrophosphate and geranyl pyrophosphate inhibit mevalonate kinase activity by binding competitively at the ATP-binding sites. Isoprenoid biosynthesis; isopentenyl diphosphate biosynthesis via mevalonate pathway; isopentenyl diphosphate from (R)-mevalonate: step 1/3. Homodimer. Belongs to the GHMP kinase family. Mevalonate kinase subfamily.