Will SIMS 4 run on this machine? I'm wary about the graphics capabilities

@Tolkienfan It will run BUT I recommend anyone who plays 3D graphical games (which is what Sims 4 is) that they get a computer with a dedicated gaming video chip. This is not required but the game will probably run better and you will have better graphics.

@Tolkienfan  Sims 4 should run on medium or maybe medium-high graphics settings if you installed most of the expansion packs, and it would perform better if you only installed a few EPs.  (Stuff packs don't impact performance much, and neither do most game packs.)  However, you could likely do better for the same or a similar budget.

If you'd like me to look for alternatives, please list your preferred budget along with any other considerations, for example storage or particular stores you'd want to use.  If you'd like to do the shopping yourself, look for a model with an Nvidia 1650 (regular or Super), ideally, or an AMD 5000-series processor if you can't find anything with a 1650.  For the latter, you'd still be dealing with integrated graphics, but the chip would be significantly faster.

Thanks everyone

Following the general advice that the machine we were looking at wasn't ideal after a lot more research we finally found this one which seems to tick all the boxes so fingers crossed.

https://ao.com/product/90n900fduk-lenovo-ideacentre-g5-desktop-black-90976-253.aspx

Next task is to work out how to retrieve saved SIMS game data from the old hard drive to put on the new PC...

@Tolkienfan  That one should work out quite well: you should be able to run all Sims 4 packs together on ultra graphics settings.

As for your game data, it's all stored in Documents > Electronic Arts > The Sims 4.  You could move the entire folder to the new PC using an external drive or USB stick, or you could upload it to a free cloud storage service (Google Drive, Dropbox, etc.) and download it onto the new computer.  You could also just transfer the saves folder and anything else you want to keep. In any case, I'd suggest zipping the folder(s) before transferring them—this helps protect some files from being altered and also saves space if you're using cloud storage.

The best practice is to launch the game once on the new computer to make sure everything works properly, then transfer the files to the appropriate subfolders within the Sims 4 folder.  That's more reliable than transferring entire folders.