Kat's W is a far better farming tool than Q. Lower cool downs and it can proc the passive you get from Q, not to mention more reliable. Max it first. It also gives you a great deal of mobility. Also, your ult already has a reduce healing effect which I'm sure you're using. The ignite would just be for the KS (Kill secure)
Gunna have to respectfully disagree. I main Katarina and play her very well. Her Q Bouncing Blades: (Should max this first)
Cooldown: 10 / 9.5 / 9 / 8.5 / 8 seconds
Dagger Magic Damage: 60 / 85 / 110 / 135 / 160 (+0.45 per ability power)
On-hit Magic Damage: 15 / 30 / 45 / 60 / 75 (+0.15 per ability power)
Total Damage: 75 / 115 / 155 / 195 / 235 (+0.6 per ability power)
Deals more damage than:
Sinister Steel (W)
Cooldown: 4 seconds
Radius of AoE: ~375
Magic Damage: 40 / 80 / 120 / 160 / 200 (+0.25 per ability power) (+0.6 per bonus attack damage)
Movement Speed: 12 / 20 / 28 / 36 / 44 %
The cooldown on W stays 4 seconds even if you max it first (which you shouldn't). Going for blades first gives you more overall damage and poke as the on-hit gives you more total damage and also scales better (higher AP ratio) than W.