It is practically impossible to say without trying unless someone sees your post and that someone is also using that specific computer. Companies like HP and Dell and others have hundreds of different models. You could try testing a few by downloading and either putting them on a DVD to test or a flash drive. Using a rolling release might be an option as you don't need to reinstall on a regular basis. Otherwise, some versions are supported for longer periods of time. Ubuntus such as Zorin are examples. Ubuntu, Mint, Kubuntu 14.04 releases will have support until April, 2019 for example. You could take a look at the distrowatch site below which has links to a large number of Linux distributions which would give more detailed info. You can read through them and compare the information there to what your needs are.