You want to send all the data to the printer.
If you have a 1000 x 2000 pixel image, there is no magic way to get a decent 3 foot print out of it.
Most prints are viewed at a distance where they take up a certain angle of your vision. You don't hold an 8x10 3 inches from your nose. So if you have an image that looks good at 8x10 at perched on the corner of your desk 3 feet away, then it will look good at 30x40 10 feet away.
The situations you watch for:
People will be closer than normal to your pic. e.g. in a stairwell, elevator, bus shelter.
People will be moving closer to examine part of your image. Tech photos, forensic photos, some kinds of art photos.
People will be much further than normal from your pic. Billboards, sides of semi trailers, bus wraps.
Most colour printing is done on a halftone grid of about 130 lines per inch. Now in halftoning you vary the size of the dot, but not its colour. So a rule of thumb is that you need about twice the pixel resolution as halftone screen frequency. So most people figure that 300 ppi is enough to get good pictures. These are ones that will not be obviously printed at normal viewing distances. (Some publications, like National Geographic use much finer halftone screens than this, and do as many as 8 colour separations. Newspapers on the other hand use 75 or 90 lpi halftoneing. Newsprint makes the ink run, so a higher frequency just makes for muddy looking prints.)
Go up close to a billboard. The halftone dots are sometimes 1/2 to 3/4 inch across.
Anyway: A 3 foot image is 36 inches. If you are going to view it close up, you want about 10,000 pixels If you are going to be viewing it from 10 feet away, 3000 x 3000 pixels is enough.