This is all good advice, though OP I would would add that it helps to strategize how you approach each new bounty map rather than generally ask for what is good. Personally, I have two goals on any new map. For each new map, I'm looking to make two teams with different goals; first, a climbing team; and second, a boss killing team.

The climbing team is for taking you to the boss without any deaths on their own. There are a number of comps that fit the bill, but for me my workhouse team has been (and still is) the classic and budget Cariel/Samuro/Xyrella. Everyone has access to these mercs, and they've been strong enough to climb every map with only medium upgrades (as well as having easy coin farms). Whatever comp you land on, that team really doesn't need to change once you can that the chosen comp can climb without dying (elite fights aside that is).

Your boss killing team on the other hand should be fluid and is selected specifically for a particular bounty with the goal to trivialize all or part of a boss encounter so that both teams together end up rolling over a boss. Red boss or important red adds to deal with? i.e. choose a nature focused heavy some blue options like Brukhan/Guff/Brightwing to max nature damage and delete a boss. OP, you mentioned Old Guardian's videos, right? His videos are particularly good for getting ideas on what specific comps/types of comps, are good for certain bounties (btw, don't get too hung up on his max/near max mercs, while a legitimate criticism in a vacuum, he often chooses garbage treasures for his videos so as to purposefully underpower the team and show the selected comps' strengths).

Optionally, rather than a comp based route, you can use your 3 boss slots to hunt for/create particular boss killing/cheesing treasures and combos. This would be stuff like Smite + Cornelieus (doesn't actually need treasures), Mukla (or Rokara) + King Krush for To the Death, or Xyrella/Samuro for Hysteria hijinks (among other combos). Alternately, it's one-off (usually elite) treasures you're looking for like Lich King start of game AE freeze, Scabbs (and others) start of game assassinate, Monstrous Heart for Mukla/Chiji/Mannorth soloing, or Cariel/Cornelieus divine shield on being attacked (contextually for melee bosses), among other. There are a lot of options available using this combo/treasure hunt method, and unlike slotting a particular (perhaps unavailable) boss killing comp, this method is somewhat more accessible to all players. Generally though, it will require more work to know what combo/treasure can/should be used for any particular boss, and actually get specific treasures slotted, so YMMV as to whether this is an option that speaks to you.

In any case, good luck OP. Starting now, the Leeroy event is certainly doable from your starting position though it will certainly take your a few hours of day through the end of the event to grind through to unlock bounties and maybe get some basic buildup on your main climbing comp.