hpst I am currently sitting in front of my old Linux Machine which I recovered from my cellar today. Chromium 68 is usable. I remember I had some bad experiences with several Linux distributions before. For the Linux world there are multiple desktop environments plus compositors, some hardware-accelerated, some not (but all on top of Linux's forced hardware accelerations).
I use Arch Linux which requires some effort to set up. Which might be an understatement for someone who just wants to use the PC already without worrying how to set up stuff like automatic mounting of USB devices and other basic things you would expect to work out-of-the-box. However, those out-of-the-box distros were pretty bad for my eyes. @Alexmam I tried Linux Mint like 2 years ago and it was one of those. Its desktop environment/compositor/whatever called Cinnamon, looked good but did not feel good. Same with Ubuntu's Unity, which is hardware-accelerated by default and lacked proper 2D support for years. I read they changed something quite a while ago so you might have a choice now. I would try Ubuntu Mate 18.04 instead of the default Ubuntu 18.04. If it does not work, you could try countless other distros, but I believe Arch could help you. The hard way is to install it yourself which force-teaches you quite a lot of how basic things work in Linux. But there is also Manjaro, based on Arch, which sets up most for you. It does not look as pretty as Ubuntu, but which distro does?
As desktop environment I use Xfce, its software (not hardware!) compositor being enabled in Applications - Settings - Window Manager Tweaks, and as browser Chromium (hardware acceleration enabled), which seem to be good currently. The "good" state might change at any time, especially on Arch, which is a rolling distro and gets updates and the latest software multiple times a day. So it is risky, and Ubuntu, IF it works, is probably more safe since almost all of its software stays frozen its current state for years. Regarding browers, there are optionally always their long time support versions which stay frozen, too.
Keep in mind if the hardware is bad for you, no software change will help you. There are those graphics cards and displays which hurt in any mode, no matter which external device - PC, console, TV tuner, whatever - you connect.
Also I still have the feeling Linux can be usable but Windows 7 is still slightly more comfortable to look at.