Alright I'll straight out say it, this will be a Division comparison, so if you don't like it, move on.
So the Division has a console in each safe house that can allow stranger players to join others, I think Bungie needs to do something similar and this is how I thing they should do it.
Note of clarification, in PvP, the system we already have puts you into a team of both and whom aren't in a full fireteam, this system will create fireteams of players where no one is by themselves. Both solo players and pre existing fireteams of less than the required amount can go through the system.
Also for both PvP and PvE will start the game after two minutes, will be so that the players can establish communications with each other. In the fireteam, there will be sub-fireteams so if the leader of that sub leaves, the rest in that team does as well. The matchmade leader is the person with the overall best connection.
Have a location in the navigation system in orbit called [i]station[/i] or whatever (the name's not important) but it is not a place you travel to, like the strike playlist, but instead when you click it, a menu similar to the player inventory system pops up where there are a variety of pre0made options (players will not be able to type anything), the first option is [i]game style[/i], (in drop box form) there are two options, PvE and PvP.
(the whole style is in drop box form)
If PvP is selected, the next option will appear, 2v2, 3v3 and 6v6. Then another option appears showing game type. It will say if the play doesn't meet the perquisites of on player and light level.
If 3v3 is selected while Trials of Osiris is on, it will also appear (but honestly, hardly anyone will pick it). The list of options will be (in order) Elimination, Salvage, Skirmish, Trials of Osiris. Normal Elimination will be on list at the same time because people might not want to play ToO.
This is the same with 6v6, the list is Clash, Control, Mayhem, Rift and the Iron Banner at the end if it is on.
Also the weekly playlist will no be featured on the list.
Obviously, no solo stuff on the list, Freelance, Rumble, etc
Now with the BIG Challenge, the PvE side of the game.
Similar options, 3 players and 6 players only (for raids, no give or take with numbers)
Remember, friends who don't need this system can select the activity as it is now.
If 3 players is selected, The Options of Strikes, PoE and Raids appear. These will be each of the lists for each of the options.
Strikes - Legacy, Vangaurd, Heroic and Nightfall (each showing the require levels)
PoE - 28, 32, 34, 35, 41, 45 (but the actual names and proper levels are featured instead)
6 players
Select out of the three, VoG, CE and KF
Select the diffculty, normal/hard. (it will initially try to find a fresh game but if unable, it will add you to a game where there is a missing member, no questions.
If there are people who strictly want a certain level guardian, I'm sorry, too bad, won't work in this system, this system is used to find a game, not a certain level, if you want a certain level, use these forums and create your own team, this goes for Trials as well.
Please Give feedback, this took a while to create. (ps I did get lazy towards the end, ask me if anything is unclear)