Value depends on condition and originality. "Matching" in the case of an M1903 means the barrel must be correct to the receiver in terms of maker and date. Stock style and stock cartouche also need to be correct fot the receiver. Bolts can be matched up by examining markings. A Remington made M1903 will show the letter "R" on most of the parts.
Distinguishing between a high number and low number Springfield or Rock Island receiver is also important.
Most M1903s were rebuilt to one extent or another during service with barrels, stocks, handguards, and rear sight components being replaced most frequently.
Photos, bore description, s/n, and barrel markings are always helpful to assist with determining originality and value.