Well since my chars are up to about 27, I don't think I've seen that yet. I don't even remember the 'legendary quests' mentioned available from 20.
Green terminals are accessible at level 20, red at about 35 to 50? and cosmic at 60.
as nickdanger said, access active quests with the L button, and at the top you can select current active Legendary quest. You will want to focus on those for now and complete them every time it resets. These are great for XP from level 20 on.
I'd suggest sticking to one of your toons now and get it to level 60, which is really easy now with the way they have boosted XP in story mode. With 1 level 60 toon, your account-wide XP bonus hits 10 or 15%. First 5 toons at 60 will net you something like 75% account-wide XP bonus. Every toon after that is +3% per level 50 toon and +5% for every level 60, maximum of 200% permanent account bonus.
If you go into your character stat screen--I think you can do this in the tabs above your character portrait in the inventory screen--you can find current account bonuses by scrolling down into the various stat sections.
This screen, if you really get into the game, you will want to be familiar with your crit chance/crit damage and now brutal chance/damage(because that is now important with Omegas and newer OP game-and-build-killing artifacts ) among other stats.
It used to be the primary goal was to hit 40% crit chance....now it is something like 80% crit with 60+ brutal or something completely insane...and I think that is now for every character because the builds have become rather flat overall (the game has always been DPS DPS DPS, anyway) --with inherent skills through character reviews and new designs, including the sweeping character-based unique sets, Hitting Crit at about 35-40% is already a given, so it doesn't require crazy high-end artifacts or much grinding now. That is why, with Omegas on top of this, Brutal is a big focus.
By the way--Omega system is a secondary tier of stat leveling for each character (Account-wide point system that you simply collect as you level all your characters and collect XP orbs anywhere. You've probably already noticed points accumulating. Yuu can set Omega levels for each character individually, from a total pool of points that is shared by all characters. It will make sense) You will be able to access this at level 30 in the P menu.
Brutal--it is basically a crit of a crit. Brutals only trigger as a %chance on top of a critical hit. So, you want both the crit hit chance and brut hit chance to be rather high. They are rather devastating--I mentioned earlier that my Kitty Pryde was Brutaling for ~4mill (or is that billion? I suddenly forget the standard) on her Phasing Samurai hits. Eventually, you want the majority of your hits to be crits or brutals--big orange numbers and especially big red numbers.
But that is end game stuff once you have your set of well-rolled uniques and decent artifacts, runewords, all of that mess. At that point, the game builds boil down to simply:"Get Moar Brutals."
Or you can skip all that mess and just level up toons, collect splinters, buy more toons.
Oh, and you will want to pick up the free Deadpool Teamup if you haven't already
https://www.reddit.com/r/marvelhero...unt_for_pirate_deadpool_achievement_spoilers/
There's actually 2 versions of DP teamup (exact same character with skills, just different costumes and dialogue) and DP is one of the most powerful, easy-mode TUs out there. Very, very useful. Especially if you want to do the cosmic trial later on, he makes it super easy for noobs once you have him leveled to 60. (His ultimate, Server Lag, is rather game-breaking)
I encourage you to work on getting him asap because TUs take forever to level.
I think you can also get the free shield agent and maybe another 1 or 2 free TUs? ...I think you can still get Howard the Duck? not sure.