The correct answer is a kinase. Kinases are enzymes that couple the hydrolysis of ATP to the addition of a phosphate group to its substrate.

Phosphatase enzymes basically function oppositely to how kinases work. Phosphatases use water to hydrolyze phosphate groups off of their substrate.

Isomerase enzymes function to interconvert the structure of molecules from one isomer to another. This means that the substrate will remain with the same molecular formula, but it will have a difference in the connectivity of its bonds.

Ligases are enzymes that work by joining two molecules together.

Oxidoreductases are enzymes that act by catalyzing oxidation and reduction reactions, which involve the transfer of electrons from one molecule to another.

The last step of glycolysis, which involves the conversion of phosphoenolpyruvate into pyruvate, is catalyzed by the enzyme pyruvate kinase, yielding one pyruvate molecule and 1 ATP. The other kinases are involved in different steps of glycolysis.

Kinases catalyze the attachment of phosphate groups to their substrates. Phosphatases specifically remove phosphate groups from their substrates, which is the opposite of the function of kinases. The other enzymes listed do not have functions that involve removal of phosphate groups. 

From it's name, we can assume that this kinase will add phosphate groups to its targets. The source of these phosphate groups is ATP. PKA has 2 catalytic, and 2 regulatory subunits. When PKA is activated, there is a conformational change that causes the regulatory subunits to fall off, and frees the catalytic (kinase) portions. When PKA is inhibited, the regulatory subunits bind to the catalytic subunits and prevent phosphorylation. PKA has many activators, but cAMP is one of the most robust and well studied activator. Therefore, cAMP binds to the regulatory subunits, but does not inhibit protein function.

Polar R-groups, namely free hydroxyl groups on serine, threonine, and tyrosine, are the usual targets for phosphorylation because they are nucleophilic and can react with the phosphate group. Other R-groups are not as reactive and therefore are not ideal sites for phosphorylation. 

One of the features of the beginning of mitosis, and various steps in the cell cycle, is the increase of cyclin activity. This cyclin controls the action of Cdk, causing changes in the phosphorylation of proteins, influencing cell cycle events. Yeast cells use one Cdk, which changes cyclin throughout the cycle, while vetrebrate cells use four -- -Cdk,  /S-Cdk, S-Cdk, and M-Cdk. No matter the species, however, Cdk binds to various cyclins over the course of a cell's life.