Because Shimano is designed to be incompatible with itself, you're basically limited to sticking to claris, or upgrading the whole system. Which would mean either going to Sora for 9 speed, Tiagra for 10 speed, or 105 for 11 speed. Once you're at the 11 speed point, 105 is compatible with ultegra and dura ace, so you can then upgrade piece by piece. A full 105 groupset is showing up as €489, vs €395 or Tiagra 4700. I can't seem to find anyone selling the Sora groupset tho. But I'd guess it's probably around the €300 mark if you can find it.
I've run Tiagra 4700 for the last 15000km, and it's been fantastic, I'm about to upgrade it, but I'm doing so because I want to go for electronic shifting, rather than because it isn't good enough.
IMHO, the difference in quality when you go from Claris to Tiagra is really noticeable, and IMHO, worth it. If your frame is in good condition, then upgrading the groupset like this, would give you the feel of a whole new bike. Change the wheels to something lighter at the same time, and you would be forgiven for thinking it really is a whole new bike.
Personally I'd upgrade to Tiagra at a minimum, and if I felt really like spoiling myself, I'd go to 105.
J