There’s a lot of approaches to preparing graphics (especially pixel-based) for presentation on the web. One of them is what zeebe suggested. Pixelmator has a good reputation, but I’m not familiar with it. I use Lightroom and Photoshop.
There is one rule of thumb: you have to find a balance between image quality and the “weight” of the file. That balance depends on what is more important to you: quality or light weight of your project. Photographers want high quality and they look at this differently than bloggers or others, who may even opt for a GIF format instead of JPEG, because for them quality takes a back-seat to space and speed. Anyway, always export photos at 100% image quality if you want crisp detail/text contained in them. If it is possible, completely avoid embedding text in your photos.
Another rule: if your photo is in JPEG format, do not try to open it in an editor, make adjustments and save it. Every time you do that, you loose quality. First time, it is a small difference, but if you do that repeatedly to the same image, you will loose more and more quality every time you save it.
And another one: if you need as high quality of image as possible, do not make an image of smaller size (dimensions) than it is supposed to appear on screen. That is especially important if your photos contain text. Let RW present them at their original size.
And last but not least, if you want your photos look great on Retina screens, make them of the appropriate resolution (144 ppi instead of 72 ppi) – that, of course will make your images twice as heavy, but the visual effect (only on Retina) is very appreciable.
I wish you luck in your visual pursuits…