Oh yes I completely forgot that bikes of that vintage aren't 9 speed. You're stuck to an alivio cassette then I guess, otherwise you also need to replace the shifter (is it any good still?). A front derailer is a cheap part. From my favourite bike part mailorder shop a Deore front mech is 22 euros, an XT mech 28 euros... I'd go for the SLX or the XT.
If it were my bike, I'd save up a bit longer for the whole lot and get:
SLX front mech - 23 euros
SLX rear mech - 40 euros
SLX shifters front and rear - 30 euros
SLX cassette - 37 euros
SLX chainring set 24-32-42 - 43 euros
Total: 173 euros for complete SLX 10-speed drivetrain minus chain and crankset (I suppose the chain you put on is 10spd compatible?).
Same list for Deore 9 speed parts (plenty good but lacks the prestige of SLX I suppose):
Deore front mech - 21 euros
Deore rear mech - 27 euros
Deore shifters - 25ish? Out of stock for 9spd
Deore cassette - 25 euros
Deore chainring set - 37 euros
Total about 137. I'd stump for the 10spd SLX instead if I were you
I'd be hesitant to buy 8 speed parts knowing you're stuck with the lower range components then and it will get harder and harder to obtain those parts in a couple of years' time. And if you tire of the frame, the SLX will be totally worth transferring over to the next one.