What aperture and ISO should I use?

I would like to take portrait photos at the beach.

I want the background, which is the sea and sand, to be totally blurred out so that the model will stand out, as I'm selling what model will be wearing.

I'm using Nikon D60.

How should I adjust my camera for such photos?

1) ISO 100-200
2) Aperture mode priority
3) spot metering mode

Set the aperture to the largest setting. This will minimize the depth of field so that the background is blurred.

You want little depth of field. To get this, set your camera at the slowest ISO setting it has. I would recommend MANUAL for everything from here on, however, most don't have a clue anymore what manual can or will do for them in a exposure, so your next best bet is to set the camera on Aperture Priority, set your f/stop to the largest opening the lens has (smallest number, like 3.5… NOT 22) and use more of 'telephoto' settings than wide angle.
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Telephoto lenses on D-SLR's are basically anything over 50 or 60mm. If you have a lens that goes out to 100mm or more, use the more. It will help keep the background really blurred and out of focus.
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Now, on Aperture Priority shooting, YOU pick the f/stop number and the camera picks the shutter speed. Because you have left the lens on it's most wide open setting the camera will pick different shutter speeds to make the different exposures. However, you may become a victim to "back lighting" where the bright back ground beach, sky or water will FOOL the meter into making a exposure for all this "extra light" and make your model dark.
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Spot metering is about the only way around this, when in any automatic mode. Close, but no cigar all the time. This is why I recommended manual "everything". Manual exposure, and manual focus.
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Good photography is not a slam bam thank you mam process. A good shoot could last for hours. Each shot is thought about but candid and spontaneous ones often the best. Automatic exposures can be fooled very well in the environment your wanting to shoot in. Hand held meters and full manual are often the tricks of the trade (as well as a few others).
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Since you don't know this, I'm going to assume that you don't know how to shoot in manual mode. So I would recommend using Aperature priority mode with as low of an ISO as possible (50-100, depending on our camera) and a low numbered aperature (2ish, or however low your camera will go.) The lower the number of aperature, the shallower depth of field, which means a blurred out background.

Slow ISO
Long lens
Large aperture (f/2.8 or similar)

The slow ISO will require more light, letting you use more manageable shutter speeds with wide apertures which separate the foreground from the background. Longer lenses also separate foreground from background. Depending on how bright your scene is, you may need to use a and filter if you wish to use fill flash.

One trick that you may not know: Along with what everyone else has been saying, do this. Put the camera in A (Aperture Priority Mode) and meter for the background. Then, pop your flash up (or use an external TTL-metering flash like the SB-600, even better) and shoot. You will find that the background is at a proper exposure since you metered there, but also the flash will have properly lit your subject. This makes for a very nice, evenly-lit photo. (if you are using the pop-up flash you may not be able to get the shutter speed faster than 1/200th or 1/250th of a second, and if you are using the external, you may have to set the flash to high-speed sync.)

Without using the flash, do what everyone else has said, meter for your subject and shoot on Manual or Aperture Priority.