Save for Web
Photoshop Elements comes with a feature called Save for Web (File | Save for Web), a slightly simplified legacy feature that was passed down from Adobe Photoshop. You would use this feature to specifically fine-tune image output so that they perform optimally in web-based media such as blogs and websites. Note that, although this is an excellent process for perfecting web-bound images, uploading to some social media sites might produce slightly different quality because those sites (such as Facebook and Instagram) might apply additional manipulation, particularly in regard to file compression, but also in relation to maximum permissible file sizes.
Before you start using this feature, it's probably best to reduce your files to a reasonably manageable size before fine-tuning with Save for Web. For most web applications, if the file's longest edge is 1,000 or 1,200 pixels, this is a perfectly sufficient resolution. It's not too big but, then again, it's not...