The Equal Protection clause provides that similarly situated people must be treated simialrly. If the law is going to differentiate, it must do so for some varying level of good reason, and all laws do in fact differentiate between categories of people, even if only between, say, murderers and non-murderers.
The Equal Protection clause provides the most protection to a “suspect class”, generally race, ethnicity, of national origin. If a state law differentiates between people based on any of these, it may only do so if it is necessary to promote a compelling interest, and the burden of proof is on the govvernment to demontrate that this standard has been met. This is nearly impossible; these laws are “virtually per se invalid”.
The next greatest protection goes to what is sometimes called “quasi-suspect classification”; for example (among other classifications), gender. These laws are only valid if they have a substantial relation to an important interest, and the burden of proof is again on the govenrment. This isn’t quite as high a standard as for suspect classification, but is still pretty high. Virginia Military Acadamy couldn’t meet it when it tried to keepout female students.
Every other classification must only meet a “rational basis” standard; the law must have some rational relation to a legitimate interest, and the burden is on the person attacking the law. That person must demonstate there is no rational relation between the law and any legitimate interest of the government.
Wealth is not a suspect or quasi-suspect classification. Laws that impact people because of their wealth must only be rationally related to a legitimate interest. Note, though, that this cuts both ways: a wealthy person cannot claim wealth discrimination becasue he pays more in taxes than a poorer person.