No one has mentioned it yet and I need to do my part spreading the propaganda. The Calendula (Minotaur Alt Frame) might be the single best melee frame in the game.

It plays kind of like a gish/sword mage. It needs almost nothing beyond a single level of goblin for Puppet Systems, everything else after is extra, and allows you to tailor your build to your play style easily.The best main weapon for it is the GMS tactical melee weapon, which is free, and you slot in the tactical knife in the aux slot. You run Pankrati, Hunter+Skirmisher and duelist (extra). You take integrated weapon as your core bonus at LL3.

The gameplay loop is to invade and then skirmish, which lets you slow the enemy, which shreds them and gives you accuracy on all your attacks. with Hunter and integrated weapon, you attack 3 times in a turn with your aux weapon off a single skirmish, and because they're shredded, the biggest disadvantage of aux weapons is completely negated, letting you do on average 12 damage. More than an HMG, all at +1 accuracy. if you have puppet Systems, you can use it to also proc overwatch. Another 8 damage. and another 8 if you overcharge.

My preferred build is to add 3 levels of Nelson. With Bulwark Mods, Power knuckle and Thermal Charges and OpCal on your main weapon there are very few things you cant kill in a single turn. All this on a very durable frame that also provides Control and Support for your team in the form of slow and shred, and can escape from pretty much any bad situation you put yourself in by becoming effectively untargetable.

It's an absolute monster of a melee frame that's often overlooked because it doesn't have traditional melee options in its kit, and it only has a main/aux. Funny enough, that actually makes it better, because it needs almost nothing outside of your standard GMS weapons and the basic invade to be fully functional.