12x18 images with 300 ppi = 12*300*18*300 = 19,440,000 pixels which is 58.2 RGB pixels = 58.2 megabytes as 8-bit, or 116.4 megabytes as 16 bits. If compressed tiff, it would be somewhat smaller based on image detail or noise.
For PSD and TIFF files, the only thing that will affect the quality of a print will be the number of pixels.
The size of the file in MB is irrelevant although it will be proportional to the number of pixels.
TIFF files may be smaller due to compression, but it is a lossless compression so, again, the TIFF file size in MB
will have no effect on print quality.
The only time that reducing the file size may affect the quality of a print is if you are printing from jpegs which use a lossy compression.