Well, first you really can get fine quality prints from a high quality jpeg, whereas many outfits don't want to deal with a tiff (and the huge tiff files if you send them a 16 bit tiff can be rather burdensome
).
As to size, if this is a DSLR image and you haven't changed the aspect ratio when cropping, then the only other consideration is whether you have enough resolution for a large image. The fact is that if the "base"/original image is of good quality/sharpness and you have not cropped too much of the image out then pretty much any of our cameras will print fine at 12x18 -- in fact I have 12x16 images I've printed from old 4 and 6 MP P&S cameras that have come out nicely and 12x18 prints from my old 8 MP 30D that have very crisp fine detail.
I don't know about specs regarding Costco, but you really should be able to export a full quality jpeg as long as it is full-size (uncropped) or, if just cropped a bit, and it should print fine at 12x18.
But, if you cropped in a way that changed the apsect ratio from the original, that will show up as something other than a 12x18. Check your crop for that aspect ratio and for not-too-close composition.
Now, some people do prefer to resize and image specifically to a certain print size and resolution, so maybe 12x18 @300 ppi. Lightroom can do that if you prefer, and in Export you can also apply output sharpening for your print-sized image. That part is up to you. Also, other than Costco (who as far as I know does not require that) there are some outside labs and commercial printers who do require this step, although for most uses, such as a home direct print, the printer "doesn't care" about the ppi, it takes an image and does its own resize/resample routine to self-optimize the image for printing.
