Changing the resolution setting does absolutely nothing to the digital image. This is a common misconception. The only thing that counts in the digital image is the pixel dimensions. Regardless of what the PPI setting is (240, 300, 600, whatever) the image still has the same number of pixels. To determine what you need for a print of any size it is necessary to multiply the inches by the desired pixels per inch. Suppose you want a 16 x 20" print at 300 pixels per inch. The math would be something like this:
300x16 = 4800 pixels
300x20 = 6000 pixels
So to print a 16 x 20" print you would need an image that is 4800 x 6000 pixels. And the PPI setting can be anything you want it to be because it has no effect on the image.
Well, how do I know what I desire in an inch? Is 300 a good number? Also I want to do this Tiff right?
Your best bet is to talk to the printer to find out what settings best meet their needs.
Output as JPG is fine. Most places don't want to deal with huge TIF files any more.
Larger prints don't require as high resolution because it will be viewed from greater distances. Images that are 16 x 20" or larger can probably be calculated at 240 PPI or even 200 PPI, and still get acceptable results. This edition to check with the lab is a good one. I think you'll find that most labs want JPEG images in the sRGB color space.