When I first started Borderlands 3, I did what I always do. I tried every character at least until I could play around with their skill of action a bit to see how they feel. I was surprised how unique and interesting each character was and especially Amara. Lilith annoyed me because of her mastery. Maya (no pun intended) didn't grab me, as her skill just wasn't much visual fun for me.
Amara however perfectly found the place for me. She has that wonderful arrogant gladiator vibe. She sold to me on the first melee hit (she hits softly). Taking a deep look at his skill trees too, I was struck by their diversity (to be fair, all of the characters look very well rounded this time around). There seem to be a lot of potential possibilities for it (I'm counting about six at a glance), but these are the three that I think are likely to be the most effective in the long run.
Beat 'Em Up
This configuration is the first that I am testing. Melee-built Borderlands games tend to give in halfway through, but I believe in this one even more than I believed in Krieg in 2.
You go deep into Brawl, focusing on damage reduction and regeneration talents first, and then speculating on Samsara, which is your daily bread. Find Your Center and Blitz are key talents. So you have to go all the way. At one point, dive into Mystic Assault for Do Harm, Restlessness, and Soul Sap. Likewise, splash some Fist on the elements to get the illuminated fist.
Here you focus on melee damage and close range weapons (shotguns, mainly). Your playstyle is to get in close, slam with your dexterity, get big stacks, hit town, rinse and repeat. Regenerating your health and reducing damage is reliable. You can use the Action skill to regain a ton of life using the Beam variant of Phaseslam, to give yourself some free time to naturally regenerate (and regain some health from damage over time) . Slam himself.
This construction excels at crowd control. But fight the bosses a bit, as your damage stacking depends on being able to hit multiple enemies. So it's probably best to use it in multiplayer.
Speed kills
This build could be more practical, but no less fun.
This one almost completely ignores the Fist of the Elements tree and goes deep into the mystical assault. You want to focus on getting crazy stacks of your Action Skill via basically all of the talents that say "Rush" on it. This skill can be either Phaseslam or Phasecast, depending on your preference. Either way, your primary goal will be to shoot guns quickly and then reload them at light speed to ensure a sustained DPS playstyle and high ammo consumption. Vladof and Dahl are your best friends for this build.
You'll want to spend Brawl on a few of the Durability and Samsara talents, as well as Mindfulness and Stamina (key talents), while mostly ignoring Fist of the Elements, except to maximize your Steady hands as you will be using a rate high fire, high recoil weapons.
You run fast, shoot fast, reload fast, and kill fast - anything a loot shooter wants, and it's perfect for speed farming or just playing the game.
Crowd control
Long-range explosive DoTs sound like fun time.
Your focusing weapons are rocket launchers and sniper rifles; these two may also be the same given some of the alternative shooting modes on the market. You tag objects from a distance with guns and then trade explosives when they come in close, causing crowds to explode and splash on you due to your investment in Arms Deal. You've got the perenniality to sustain yourself long enough for contagious DoTs to do their job, and you'll subjugate more with the mystical assault tree's action flight skill, Soul Soul.
Your main focus is Fist of the Elements, a talent that increases the damage and spread of your DoT damage. You enter Brawl for as long as you want, and at one point, grab some Mystic Assault talents to collect the previously mentioned Soul Sap.
This one should be ideal for solo play primarily because it combines sustain with severe damage to one or more targets.
These are the three builds that I see to be the most important at the moment, but things could change as the cap level increases (assuming it does) and more skills are added.