One of our earliest looks at theatre in the US comes from William Dunlap’s A history of the American Theatre, published in 1832. In it, he presents the following salary information, which we can glean some insight on to how props were acquired and who was in charge.

The theatre of New-York had now but one director or manager,—a circumstance which had not occurred in the United States before. An estimate of the expenses of the theatre at this time, 1798-9, will perhaps be acceptable to the general reader, and useful to those concerned in similar establishments. The salaries to actors and actresses, as follows, amount to 480 dollars weekly, viz: Mr. and Mrs. Hallam, 50; Mr. and Mrs. Johnson, 45—the first 20, the second 25; Mrs. Oldmixon, 37; Mr. Cooper, 25; Mrs. Melmoth, 20; Mr. Tyler, 20; Mr. Jefferson, 23; Mr. Martin, 18 (and for superintending the stage and making properties, 7 more); Mr. Hallam, jun., 16; Mrs. Hogg, 14; Mr. Hogg, 13; Miss Westray, 13; Miss E. Westray, 12; Mr. Lee, 12, as performer and property-man; two message carriers (each 8), 16; Mrs. Seymour, 16; Mr. Seymour, 9; Mr. Miller, 12; Miss Hogg, 4; estimate for three others, 54 ; Mrs. Collins, 12; with supernumeraries, 32. To this was added a wretched prompter of the name of Hughes, at 10, and an intelligent box-office keeper, Mr. Joseph Falconer, at 14. Dressers, 20; orchestra, 140 (consisting of Mr. James Hewet, as leader; Messrs. Everdel, Nicolai, Samo, Henri, Ulshoeffer, Librecheki, Pellessier, Dupuy, Gilfert, Nicolai, jun., Adet, Hoffman, and Dangle). Other expenses were estimated thus:— Lights, 109; Labourers, 24; Doors and Constables, 50; Cleaning, 5; printing, 68; properties, 6; wardrobe, 15; fires, 15; Mr. Ciceri and his department (the scenery and painting, not including materials), 60; rent, 145; amounting to $1161, without including any remuneration for the personal services of the manager. (Dunlap, pg 248)

[emphasis mine]

From that, we can see that one of the actors in the company received additional compensation for superintending the stage and making the properties. I’m not sure what “superintending the stage” actually means, since another person is listed as the prompter, which I thought to be the person managing the rehearsals and performances. Another actor served a dual role as performer and property-man, though no extra salary, probably because he plays only minor roles. Finally, there was an estimated $6 spent per week on properties, though whether that is for buying and renting items, or for materials to make them is not stated.