The challenge with a Battlecruiser with long range medium weapons in a Level 2 mission is you will face a lot of frigates that you can’t track on when they have closed you down.
This is the sort of fitting I first ran Level 2 missions with - if you have reasonable drone skills then it should serve you well.
Arbitrator
[Arbitrator, L2 mission]
Damage Control I
Drone Damage Amplifier II
Drone Damage Amplifier II
Compact Multispectrum Energized Membrane
Medium ACM Compact Armor Repairer
10MN Monopropellant Enduring Afterburner
Medium Cap Battery I
Cap Recharger II
X5 Enduring Stasis Webifier
Drone Link Augmentor I
Drone Link Augmentor I
Focused Anode Medium Particle Stream I
Focused Anode Medium Particle Stream I
Medium Thermal Armor Reinforcer I
Medium Explosive Armor Reinforcer I
Medium Kinetic Armor Reinforcer I
Hammerhead I x5
Hobgoblin I x5
Hornet I x5
Vespa I x5
Multifrequency M x2
Radio M x2
Standard M x2
Currently about 25m ISK on Amarr market prices. More if you can fly T2 drones or upgrade some of the components. I suspect 25m ISK is the going rate for a modest fit - I’d be thinking nearer to 30m ISK or more.
I’m suggesting an Arbitrator since if you are stronger in drones it will give you the best punch - the secondary weapons I’ve put on it are lasers as you will want to train them up for a Maller or Omen later on, but you could go with three missile launchers instead - Heavies/Assault/Rapid Light depending on your preferences.
If you do go for an Omen or Maller as a first T2 mission ship, the fit it with Pulse Lasers and consider adding a Webifier and/or Tracking Computer to give you a better application against small ships.
Drones on the Omen and Maller are very much a last resort weapon - I normally don’t bother deploying them unless I’m really after damage dealing.
Beam Omen
[Omen, Omen - PVE L2]
Reactive Armor Hardener
Tracking Enhancer II
Heat Sink II
Heat Sink II
Medium ACM Compact Armor Repairer
Compact Multispectrum Energized Membrane
Medium Cap Battery II
Cap Recharger II
10MN Monopropellant Enduring Afterburner
Focused Anode Medium Particle Stream I
Focused Anode Medium Particle Stream I
Focused Anode Medium Particle Stream I
Focused Anode Medium Particle Stream I
Focused Anode Medium Particle Stream I
Medium Auxiliary Nano Pump I
Medium Capacitor Control Circuit I
Medium Capacitor Control Circuit I
Hobgoblin I x5
Multifrequency M x5
Radio M x5
Standard M x5
30m ISK which happily ignores what I said above - but focused medium beams track better, and I’ve put a tracking enhancer in lows - This is for missions with frigates in them: application is important. Hence the full flight of five light drones rather than four mediums that it could also have.
The best upgrade to that Omen is to use Navy Crystals with it - they are more expensive but give you another 15% damage.
A good destroyer, flown well can do Level 2 missions, so an Omen or Arbitrator should be comfortable for you. Just don’t spend all your ISK on one ship! Only fly what you are happy replacing: it’s rough out!
Hopefully useful as a starting point before everyone piles on with their own equally individual opinions.