@timc1966 Sorry for the delay. I finally got a chance to look around a bit, and I think you can do a little better than the options you've found.
Among those three though, the first one is clearly the best as-is. The second one would be better if it had 8 GB RAM instead of 4 and if you could add a better graphics card—the GT 710 is much slower than the integrated graphics chip in the first desktop. But without seeing the price on the second build, I don't know whether that's feasible. As for the third option, laptops don't perform as well as desktops on most tasks, hardware being otherwise equal. You also can't usually upgrade a laptop's processor or graphics card, unlike with a desktop, and it's much harder to repair a laptop as well. So if there's no compelling reason to get a laptop, a desktop is the better option.
I did see a couple desktops that would do better than the first one you found though. The same company that makes the gaming PC you saw also offers this system, with a stronger processor and a faster integrated graphics card. It also has a power supply that would support a mid-range dedicated graphics card, if you or your daughter decided to upgrade at some later point.
https://www.awd-it.co.uk/awd-stronghold-ryzen-5-3400g-with-amd-rx-vega-graphics-desktop-pc-for-gaming-if10.html
This computer doesn't come with a monitor, but you can find good ones for £80-90. These all have IPS panels, the highest quality screen, and are almost certainly better than the one included in the bundle from Costco.
https://www.box.co.uk/22MN430M-B-LG-22MN430M-B-21.5-Full-HD-IPS-FreeSync_2930964.html
https://www.box.co.uk/LG-22MK400H-B-22-Full-HD-IPS-FreeSync-7_2401606.html
https://www.box.co.uk/ASUS-VA229HR-21.5-Full-HD-IPS-75Hz-Moni_2734511.html
Even cheaper would be this Lenovo, with the same processor and integrated graphics card as the one above. It would be much more difficult to upgrade though: the case doesn't have as much room, and the power supply would need to be replaced as well, and the new PSU connected to the various components.
https://www.box.co.uk/Lenovo-V55t-15API-11CC0009UK-Business-_2845879.html
Custom computers on other sites are either a little or a lot more expensive for the same components, but let me know if you'd like to see other options.