What is the best way to preview and save images for the web?

Couple of things to consider regarding embedding the sRGB profile in your web images:

• only desktop OS users with a properly profiled screen AND a colour-managed web browser will benefit from embedded profiles. This is not the case for the majority of users (90% or higher).
• Only Safari on MacOS is by default colour managed, as far as I am aware. For other OSs and browsers the user must turn on colour management, and find an obscure setting to change it.
• browsers running on mobile devices are not colour managed. 100% of mobile browsers will not use that embedded sRGB profile. Most mobile screens are very close to sRGB anyway.
• embedding a colour profile increases the file size of an image by around 4K.
• embedding profiles in a web image may result in colour inconsistencies between Windows/Linux and Macs, resulting in colour differences between (for example) a html page's background colour and the image's background colour that should blend seamlessly. As far as I am aware, most colour-managed web browsers only colour manage tagged images, not the entire browser output. Firefox is the exception here, and keeps things "colour consistent and correct" whether things are tagged or untagged and colour-manages everything in the page.
• with wide-gamut screens you MUST tag the images and enable colour management in your browser for correct colours.
• Most web users couldn't care less about correct colour or colour consistency. If we tag them sRGB, it is because WE care, as "professionals".

If you'd be creating hundreds of thumbnails on your site, and each thumbnail is only a couple of Kilobytes, then embedding the sRGB profile is going to really blow up the overall data bandwidth unnecessarily. Colour consistency/correctness probably isn't important anyway for small thumbs, so in this case I would just remove any superfluous metadata, including the color profile data. When the user opens the original larger image, then I would keep the profile, of course.

If I am building a web app only used on mobile screens and browsers, I would also remove any embedded meta data and colour profiles. It's not used on mobile browsers, and only increases the size of the GUI elements. Besides, the question pops up whether it is important to put color profiles in images that will be used for GUI creation only, since browsers will treat those implicitly as sRGB (as far as I am aware), and no-one will care if the overall GUI's colours shift a bit around. In particular when that application is going to be used under vastly different lighting conditions and sub-par screens.

I would go one step further and state here that if your target audience is mobile browsers and users, embedding sRGB profiles (and other ones) in your images is a waste of time, energy, and bandwidth, because the screens and browsers aren't colour managed, the viewing conditions alternate between vastly varying conditions continuously (even within seconds when traveling), and its users couldn't care less about whether the images they view are "colour correct", or not. They are only interested in content consumption.