As Scott pointed out: the only way to change proportions is to crop, but you can size the item as close to one of the desired final pixel dimensions first, and then crop.
For a naive (mechanical) way, you merely set the smallest dimension of the original image to the correct size for that dimension. The other dimension will be larger than the desired final size on that axis, so you can crop to the image. Many (most?) photos have the focus in the center, so you set up the crop so that the edges are cut (crop to the center).
As far as resizing without quality loss, all resizing is a loss in quality. Sizing down throws away data, and if you are not resizing by a factor of two in both directions, there must be some math involved that decides how to deal with it. Downsizing is usually OK even by larger percentages, but the image will become blurry.
Upscaling by more than 50% or so should be avoided, since you will be enlarging the flaws in the original image as well as adding new flaws.
Exactly how much you can get away with in either direction is going to be a personal decision, but I will say that when I get images too small for the desired placement, I groan, something I do not do when I have to downsize.
Any automated process where the multiplier is in the range of "original image dimension times (.5 to 1.5)" is probably going to be fine without user intervention.