I can almost guarantee the OP will not be able to find a proper tuxedo for rent, which is the main factor in my decision to buy vs. rent. Joseph A. Bank has a proper tuxedo available for $299 right now. It is the Signature Peak Lapel model, which is a 1-button peak lapel tuxedo with grosgrain facings. It was the only one I could find like that for under $1500.
They do not have a proper vest or a decent pique shirt through. Charles Thyrwitt has a nice marcella/pique shirt in either turndown or wing collar. A proper low-cut vest with lapels is going to be very tough to find. A cummerbund is the simple solution, though a vest is traditionally used with a peak lapel jacket and a cummerbund with a shawl lapel.