https://helpx.adobe.com/illustrator/system-requirements.html pegs it back to a machine we saw in 2000 with a Pentium 4. Almost any laptop today exceeds what I read there.

You did not reveal your country but for 350 Euros this fits.

http://www.amazon.com/Best-Sellers-Electronics-Laptop-Computers/zgbs/electronics/565108
The current #1 is http://www.amazon.com/Toshiba-Satellite-C55-C5241-Laptop-Intel/dp/B010SBAJDS/ref=zg_bs_565108_1 which was 450USD or 400 Euros.

Maybe the i3 will cut the price but later you can change the HDD to SSD for an upgrade.