A word or phrase to describe people who are practical and "care more about themselves"?

Machiavellian describes someone who manipulates situations to their benefit, using human emotions when suited, and dropping them when not.

An opportunist is "someone who takes advantage of any opportunity to advance his own situation, placing expediency above principle"; ie someone who stoops to almost anything to gain an advantage.

Ruthless means, in part, "not thinking or worrying about any pain caused to others"; for example, She ruthlessly pursued her ambition, letting nothing get in her way.

A selfish person is "concerned with oneself or concerned with one's own interests, especially to the exclusion of others."

Per previous answer, a Machiavellian person tries to achieve goals by cunning, scheming, and unscrupulous methods. If you want to suggest lack of scruples, opportunist and Machiavellian do so. If you don't want to suggest that lack, ruthless and self-serving may be a tiny bit better. (I slightly prefer the term self-serving to self-centered in this context.)

OP tells us approximately what kind of behaviour he's talking about, but the choice of adjective depends very much on the attitude of others to that behaviour.

For example, Tom could be described as pragmatic, focussed, objective, goal-oriented, etc., by someone who either admires him or is simply offering a neutral description. But someone who doesn't approve of the way Tom acts might say he's self-centred, self-obsessed, egotistic, etc.

In the final analysis, all such words are somewhat vague. It might be, for example, that OP specifically wishes to call attention to the fact that Tom's behaviour is often manipulative.

A person who is 'pragmatic' in this way could be described as self-interested.

From the ODO:

Motivated by one’s personal interest or advantage, especially without regard for others.

An example:

Years of observation and introspection have led many to the conclusion that people are self-interested creatures.