Your image is not 1500px at 96DPI. It is either 1500px wide and whatever that means depends on the screen resolution in use, or it is 15.6" wide at 96PPI.
The best way to determine if an image will look good in print at a given size is to first determine what the DPI resolution of your screen is. For instance, my MacbookPro Retina is running at the default "pixel doubling" resolution of 102DPI (1440x and it is 14" wide).
Then view the image at the largest size where it looks good to you, say that is 100% zoom. If you have 1500px long edge and it looks good, then it is 1500÷102DPI=14.7" print at 102PPI. If it looks good at 200% then you can print it 2x as large. If the image begins to pixelate (e.g.300% zoom) then you have reached the limits of the PPI resolution.
Technically, if the image is going to be viewed from a greater distance then you can get away with a lower print resolution; E.g. a billboard @ 10DPI.
Personally, I try to stay at/above 150PPI for quality prints, but I have printed at lower with decent results... this all really depends on the physical size and quality of "the negative" you are starting with more than anything else. I.e. you can have a 50MP image of crap, and it will print as crap regardless of the output size.
Depending on the printing method/medium (e.g. inkjet on canvas) you may be able to print a little larger at a lower PPI. And if you are not knowledgable about sharpening for the particular printing method/medium, you might want to print a little smaller. But in either case, it should be very close to what you see on screen.
The 300PPI recommendation most reference is because that closely matches the approx 300dpi maximum capability of most printers; but that does not mean you will be able to see it (you won't, not w/o magnification). The printer will use its' maximum DPI regardless of what you send.