I'd go for Mint with XFce or xlde/lxqt for this one, or Lubuntu. Basically, you need anything that uses less than 700 MB of RAM (ideally around 350, like the Raspbery Pi version of Debian, but that doesn't exist in the x86 world unless you go really low end, like DamnSmallLinux), and then you need to be very careful to not open more than 1-2 tabs on your browser, or you will start swapping. The biggest problem on your PC is not the speed, neither the size of the drive. It's the 2 GB RAM. It's a strict minimum of 4 GB these days to do adequate web browsing. But it's still possible with 2 GB if you're very careful what you're loading, and how many tabs you're using. My mom's laptop has 2 GB of RAM too, and it's equally slow in CPU speed, but it works for her, because she doesn't know how to use tabs (she uses the browser with a single tab), and that's enough at 2 GB.

And I know what I'll suggest next is an anathema in these parts, but it's true: Chrome uses less ram (there's even a setting for it) and it's significantly faster on older computers than Firefox. I have put together at least 8 old computers with Linux for friends and family, and that has been my experience consistently. On newer hardware it doesn't make much of a difference, but on old hardware (e.g. anything less than 1500 Passmark CPU points, like yours), it does, visibly so.

Other suggestions: turn off start-up services on the xfce prefs about services you don't need. For debian xfce, you will also need to edit a text file for policy-kit (somewhere on /usr) to make the laptop sleep on its own without intervention (otherwise it will tell you that it doesn't have permissions to do so). Finally, Chrome might not load up on debian xfce, you will need to edit the launcher to include the basic password store chrome option, to make it load. Other ways to save RAM on xfce: include only 1 panel, don't use applets you don't really need, and use a color instead of a picture for background (you will be amazed how much ram that takes!).

Final advice: update the bios firmware via windows before you delete it. This will allow you to disable the fwupd service on linux, to save more ram (there are not going to be any new versions for that old model anyway).