O don't want to discourage you from upgrading, but keep in mind that if you spend a lot you'll end up with a fairly expensive, but essentially cheap used bike.

Brakes are a straightforward upgrade, and you don't have to replace the levers to make the change. Odds are the better brakes won't stop better, though they might, but they'll be easier to keep in adjustment.

The cassette and derailleur is where you have to do lot's of soul searching. To go from 6s to 8s, will probably require (besides the cassette) a new rear wheel, a new derailleur, and definitely new shift levers (or combined brake/shift levers). This will add up to fairly serious dough, and combined with the brakes and labor could exceed what you spent in the first place.

Also consider that bikes are built with frames and components somewhat matched in quality, so those parts you didn't change will become problems down the road and begin to need replacement or repair, and you'll still be riding a fairly basic bike.

Before spending a Euro on upgrades, work up an analysis of what the total will be and compare that to what a decent upgrade bike would cost. If the money is anywhere close, stay with what you have a bit longer, doing only what's necessary to keep it rolling, and save the money for a replacement bike when you're ready. This bike can then become a bad weather or utility bike, or you could sell or trade it toward paying for it's replacement.

As you've no doubt learned by now, the most important upgrade to a bike like yours is the engine, and I'll bet that's happening already. pretty soon the hills will get flatter, and the need for upgrades may disappear anyway.