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The only thing that matters for web use is the pixel dimensions. DPI or more correctly, PPI, doesn't mean a thing. A 1200 x 800 pixel image at 300 ppi will be the same size on a monitor as it would be at 96, or anything else. PPI is only a tag for printing. For printing, you need enough pixels to print at your desired size in inches at the ppi desired. For example, using 300 ppi, an 8" x 12" print would require a image that was 2400 pixel x 3600 pixels. For set dimensions in pixels, the higher the ppi, the smaller the print. Noise isn't a factor.
Crop your print to the needed ratio (if needed) and send them as much native resolution as your image has. Unless you are sending absolutely massive files, there is no downside to send the file at native resolution (cropped of course if necessary to meet the print ratio) when printing. Sending too little, on the other hand, is an issue. 300 ppi is generally considered the standard for a closely viewed print. A lot of images can be printed with only 200 ppi and still look acceptable depending on subject matter, but you are now cutting it close for more intimate viewing. Anything over 300 ppi just gives you and the lab some extra cushion. Noise should only be an issue if it was an issue in the original image and not addressed in post processing.
In general, that is my experience too. The one big exception I find is that gmail uses the DPI value with embedded email images. My birding companion uses 96 as a default with his images and when he sends me a shot it is HUGE in my email. If I click on it to view it, it is sized normally. I use 300 as my default and my images embedded in gmail are displayed much smaller. FWIW
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