Too many unknown variables. In general, your highest DPS is going to be blasters with short range/high damage ammo. Unless you can use Trig Disintegrators and give them time to spool up. Both options are quite short range, and in general all ‘highest DPS’ options will be short range.
So unless you’re talking about a ‘mass raging battle’ that can all be fought at a range of a few KM, you’re not talking ‘highest DPS’. You’re talking ‘what is the most DPS that can be worked into this type of battle fought by these types of ships at this approximate range with this sort of support?’.
Catalysts are a cheap blaster DPS ship. Check zKillboard for cheap fits.
For part of your question, “your only mission is to put as much hurt for as cheap as possible”, you’re not actually even looking at DPS. You’re looking at Alpha Strike. DPS is sustained damage over time, but damage over time can be healed or resisted over time. Alpha Strike is one-shot big badda boom. With the goal to blow the target off the map before it can be healed. A ship gone hurts more than a ship your support is struggling to heal.
There’s also the issue of ‘damage application’, which involves how well your weapons actually deliver their potential DPS to the target. Which again, means the target(s) needs to defined as different systems will apply differently, and different ships will allow different DPS/application mixes.
“Most hurt for cheap” will generally involve T1 hulls with the most high slots for turrets/launchers. So Destroyers and Attack BCs will pull ahead. But they’re the weakest in defense also so easily destroyed. So ‘cheap’ becomes a question of “how many cheap ships will you throw away before it stops being cheap?”.
EVE doesn’t have tidy answers for all these “what’s the best?” questions. Every day in help you see “what’s the best X?”. There is no best. There is only “what’s good for this situation under these conditions given these constraints?”.
TL; DR: Short range weapons have the highest DPS. Pick the short range weapon and ammo combo that delivers the highest DPS or Alpha, that matches the range you want to fight at.
For ‘cheap’ weapons (ie. not Disintegrators etc.)
Short range: Blasters, Autocannon, Rockets
Medium Range: Pulse laser, Light Missiles
Long Range: Beam Laser, Heavy Missile, Railguns, Artillery, Cruise missile
Not definitive, but that’s the general idea for cheap stuff.