When I want to upsize an image then I always start with the raw file. Usually I shoot RAW+JPEG so I have an in-camera JPEG file and a raw file of each shot. I often end up using the JPEG ... but not for upsizing.
My preferred raw converter is Adobe Camera Raw which has a resample feature built in so it can do up- and downsizing at raw conversion time. However I don't use it as it introduces tiny ringing artifacts around high-contrast edges. Apart from those artifacts, the resampling result is the same as Photoshop's resampling method Bicubic Smoother.
So I convert to the camera's native size into TIFF format. I don't let ACR apply any sharpening but I do use some of ACR's color noise reduction (strength 4 - 8; the default of 25 is waaay too strong). Before ACR 4.1, the sharpening was too coarse so I never used it. ACR 4.1's sharpening now is much better so I may adopt it eventually but have not yet changed my established workflow.
Before upsizing, in Photoshop I always pre-sharpen the image by applying Sharpening For Source as described in Bruce Fraser's book "Real-World Image Sharpening." It basically is Unsharp Mask with a high amount (200 - 400 %, depending on the camera's AA filter characteristics) and a small radius (0.4 - 1 pixel, depending on the camera's pixel count), applied to the medium tones only (using the 'Blend If' sliders) through an extra layer in 'Luminance' blending mode. Note that this is NOT the same as Capture Sharpening which would be Sharpening For Source and Sharpening For Content combined.
Upsizing the pre-sharpened image will retain more detail than upsizing the unsharpened image. That's because the upsizing process will 'flatten' the unsharpened details so after upsizing they won't be accessible to sharpening anymore. Pre-sharpening the details before upsizing will greatly reduce this unwanted effect. For the actual upsizing I use Photoshop's Image Size command with resampling method Bicubic Smoother. After upsizing, Capture Sharpening will be applied.
It doesn't matter whether tone and contrast adjustments are applied before or after upsizing. The majority (if not all) of these kinds of global adjustments should have taken place in the raw converter anyway. It seems to be a good idea to apply delicate local adjustments---in particular those that incorporate paths, selections, and/or masks---to the upsized image, for exactly the reasons pointed out by 'pfigen' (see above).
-- Olaf