For Army, the following ranks are encountered.
Where not otherwise noted, the source is EU C canon. Details of the rank mostly come from Rebellion Era Campaign Guide, unless otherise noted.
Corporal: Second-in-command in a squad of nine troops. The corporal was the senior-most trooper.
Disney Canon appearance: Aftermath
Sergeant Major Jom Barell of New Republic Special Forces (SpecForces) looks to the five men and women standing to the right of him at the open door. On their torsos sit carbon-lace armor, the shoulders marked with the sigil of the New Republic: the Alliance starbird, now inside a sunburst. The symbol of a changed day, a new dawn. The phoenix, truly reborn.
The soldiers standing here with him: Corporals Kason, Stromm, Gahee’abee, Polnichk, and Durs.
Sergeant: Commanded a squad of 9 troopers.
Disney Canon appearance: Star Wars Rebels: The Siege of Lothal
Sergeant Major: The most senior NCO.
Disney Canon appearance: Aftermath. See above quote.
Lieutenant: Commanded a platoon that consisted of 4 squads (36 troops).
Disney Canon appearance: Empire Strikes Back.
A Rebel lieutenant moves to Major Derlin, an officer keeping watch with the princess.
Captain: Commanded a company that was made up of 4 platoons (144 troops)
As in real life, there's a difference between an Army rank of "Captain" (an officer between Major and Lieutenant rank), and Navy rank of Captain, who is a commander of (star)ship of ANY actual military rank or seniority - e.g Solo was a Captain in ANH (of Millenium Falcon), as was Needa (of Imperial class Star Destroyer).
Disney Canon appearance: Empire Strikes Back.
A captain issues instructions to two of his men at the entrance to the main transport bay.
Major: Commanded a battalion composed of 4 companies (576 troops)
Disney Canon appearance: Empire Strikes Back.
A Rebel lieutenant moves to Major Derlin, an officer keeping watch with the princess.
Colonel: Commanded a regiment that was made up of 4 battalions (2,304 troops). Occasionally commanded brigades which was composed of 4 regiments (9,216 troops). The colonel was occasionally referred to as a regimental commander
Disney Canon appearance: Iffy.
Airen Cracken was a Colonel from EU info (details shown here, but seems to be confiemed by Kenner toy), and was in a deleted scene on a Falcon during battle of Endor in ROTJ. BUT, he was uncredited according to IMDB, and I can't find any script or novelization confirmation of him or his rank. And Leland Chee seems to think he was a General in the first place! (see below for blog link)
However, if we also count Disney Mobile games as Disney canon, "Star Wars: Commander", Jennica Pierce is a character in a game who's a colonel. She's in a SW databank but without a rank listed there.
Commander
Disney Canon appearance: ESB. Luke's rank.
RIEEKAN: Commander Skywalker reported in yet?
I'm still at a loss to see just who Luke actually commands.
In addition, Leland Chee posted this blog entry "General Solo's Rebel strike team" on Keeper of Holocron blog... I'm not quite certain that it rises up to Disney canon, but it's still Leland Chee!!!
**Major** Bren Derlin (mentioned in early script but not seen in film) [GG5]
**Lieutenant** Page [GG5]
Lieutenant Greeve [GG5]
Lieutenant Nik Sant (he's the guy that puts on the biker scout uniform)
**Sergeant** Bruckman
Sergeant Junkin (sometimes sports a goatee) [GG5]
**Corporal** Beezer [GG5]
Corporal Janse
Corporal Kensaric
Corporal Delevar [GG5] (aka Sergeant Brooks Carlson?)
I speculate that these are actually the same actor.
The bad news is that the same blog post calls Cracken a "General", not "Colonel".
Now, to address your remarks of how much high brass the Rebellion has:
I found it notable, that among the Rebels, we have Admiral Ackbar, General Calrissian, and General Solo. Apparently it's not very difficult to attain very high ranks.
Admiral Ackbar commands entire Rebel Navy/Fleet. That is quite an appropriate rank for someone in his position. He's also the pre-eminent strategist and tactitian in the Rebellion, and probably their most talented naval officer at that time.
Lando was made a general because of his prior military accomplishments (details are covered in James Kahn's ROTJ novelization) as well as his role to lead all fighters in Endor attack:
Lando laughed affectionately. “I’m a man of many faces and many costumes. Someone must have told them about my little maneuver at the battle of Taanab.”
Taanab was an agrarian planet raided seasonally by bandits from Norulac. Calrissian—before his stint as governor of Cloud City—had wiped out the bandits against all odds, using legendary flying and unheard of strategies. And he’d done it on a bet.
Of course, he was also in charge of military operation to evacuate Cloud City at the end of ESB, outsmarting Vader.
Han Solo... well, my personal opinion is, that's just plain out nepotism. His girlfriend got him the job.
Having said that, Han has ample military experience. He organized and led a full scale military operation before (defense of Nar Shaaddaa against an Imperial attack).
As for "not very difficult", we only have 1 named and known admiral in original trilogy (Ackbar), and 4 named and known Generals (aside from Solo and Clarissian, we have Crix Madine and ESB's General Rieekan) and presumably some unnamed generals serving as Ackbar's staff (novelization mentions their existence but not names or even count)
The Force Awakens update
Rebellion officer ranks are listed in The force Awakens Visual Dictionary:
General/Admiral; Colonel, Commander, Major, Captain, Lieutenant: