Generally in Linux older hardware is well supported. You are more likely to run into device driver issues with bleeding edge hardware. Most likely the hardware in these laptops will be well supported, though there can be something that will be harder to get working (like perhaps an old Broadcom wireless card).
One issue you might run into with older hardware is RAM. If you have at least 1GB, then you should be able to run one of the slightly lighter distributions like Linux Mint XFCE (as mentioned in the article), Xubuntu, or LXLE. If you have less than that, these distributions may still work, but not as well. I don't recommend using a really outdated version of Linux, but there are distributions that work well on very little memory, like Puppy, or if you have not quite so little perhaps something like Salix Openbox. The advantage of using one of the Ubuntu based distributions (like the first group I mentioned) is that they have extensive software repositories.
I have done a bit of experimenting with low powered hardware, and I have found LXLE to be a good way to get an up to date Linux distribution on hardware that might be a bit slower running Linux Mint XFCE. Besides these two distributions, Xubuntu or Ubuntu Studio (also XFCE based) are not bad choices, and I've used them quite a bit. Lubuntu can be OK, but I have had fewer issues with the Lubuntu based LXLE. Of course for really underpowered hardware, you will have to go to one of the specialty distributions like Puppy.
Generally in Linux older hardware is well supported. You are more likely to run into device driver issues with bleeding edge hardware. Most likely the hardware in these laptops will be well supported, though there can be something that will be harder to get working (like perhaps an old Broadcom wireless card).
One issue you might run into with older hardware is RAM. If you have at least 1GB, then you should be able to run one of the slightly lighter distributions like Linux Mint XFCE (as mentioned in the article), Xubuntu, or LXLE. If you have less than that, these distributions may still work, but not as well. I don't recommend using a really outdated version of Linux, but there are distributions that work well on very little memory, like Puppy, or if you have not quite so little perhaps something like Salix Openbox. The advantage of using one of the Ubuntu based distributions (like the first group I mentioned) is that they have extensive software repositories.