Go to Aperture/Preferences/Export
Half way down the menu set Email Using: to your email host
Select the Email Photo Export preset and scroll to the bottom of the presets list, select Edit
In the Edit menu set:
Image Format: JPEG
Size to: Fit within (Pixels)
Set Width 2400 and Height 1600
DPI: 300

I had trouble following John’s instructions. I think it’s a little more complicated than his instructions show. Let me add my own.

1. The first thing you need to do is create an export preset that matches your requirements.
Aperture->Presets->Image Export…

2. Select one of the existing presets that starts with “JPEG - Fit within” and click the plus button at the lower left corner of the Image Export dialog. This will create a copy of the selected preset that you can change without losing the existing preset. Rename the preset to something that reminds you of what it is for. You’ll now edit the settings of the preset on the right.

Note: You should avoid editing existing presets without copying or changing the name or some day you will chose it based on the name but the results will be different.

3. Make sure the Image Format is JPEG.

4. Set the image size to something like 10. You can adjust this later if your resulting images are bigger than 5MB. There is no control for the size of the file.

5. Set the Size To: popup to “Fit Within (Pixels)”

6. Now what width and height do you use? This is a little tricky. Your requirements are for an image size of “at least 1600”. Unfortunately, the Aperture fit within function does the opposite. It does “fit within” which would be “at most 1600” rather than “at least 1600”. You need to do some calculation here so that you can create a preset that handles both portrait or landscape images. And you need to know the aspect ratio of your images.

Example: If you shoot a DSLR your images probably have a 3:2 aspect ratio. That means an image with a 1600 pixel shorter side will have a longer side of 2400 pixels (1600 x 1.5). If you enter 2400 for both height and width in the preset, then it won’t matter which orientation your images are. They will all come out either 2400 x 1600 or 1600 x 2400.

So the simplest setting for you (assuming DSLR 3:2 aspect ratio) is 2400 x 2400.

If your images are of varying aspect ratios, things get more complicated for sure.

7. Click the OK button on the Image Export dialog.

8. Now what ever method you use to get the image out of Aperture (email or export version), use the preset you just created. If using email, you first need to set the email settings in Aperture->Preferences->Export.

Note: One other gotcha: If you use Apple Mail, there are image size settings within a new mail message. Make sure to set it to Actual Size or Mail will further reduce your image size when sending it.