If you are willing to take the long game, I would focus on NOT ranking up quickly, and gathering item pieces form the shops. If you are patient (and active), you can gain a lot of rares in a decent amount of time, depending on your standards.
Personally, I'm the happiest right now with double mortars+cannon+big torpedo. Shooters are supposed to be in the back, so the cannon is for when enemies come to me. However, this is in large part because I spent a bunch of time collecting items, even epic ones, and both my mortars are epic, if low level.
Your playstyle might work better with a different setup. Either way, I would strongly advise against having more than 1 short range weapon. Shooters are long range artillery. So with your setup, I would set the cannon and ballpark mortar on, while taking the blast cannon off. Blast cannons won't shoot over walls. Mortars do alright damage from a distance, and both them and torpedoes are very good in team fights, once you get better at positioning.
Replace your bandage with a turbo. Way too easy to take damage without it.
You want to be able to cycle between three of your items relatively quickly. Don't make all of your items high-risk, high reward, or you will have really unpredictable and inconsistent results. The cooldowns are too punishing if you miss.
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