Protector is a good mechanic check for your raid, while also not requiring much gear. The next would be Galakras, then either Pride or Juggernaut. Juggernaut is mainly a healer check, a lot of guilds actually 4 heal it for progression.
I believe my order was something like Immerseus -> Norushen -> Protectors -> Galakras -> Sha -> Shamans -> Nazgrim -> Malkorok
Juggernaut was after Malkorok for no particular reason, we just never attempted it. It's definitely similar difficulty with Sha though. Shamans is probably the same difficulty or harder than Malkorok with two tanks, instead of three. Three tanking trivializes half the mechanics.
We went in order of bosses immerseus > protectors > norushen > sha > galakras > jugger . The path has not been easy, but it forces each and single raider to be at their best to get a boss down.
For you it'll probably will depend on the strength of your raiders and what you have available.
Take protectors on next if you have 3 healers (2 for farm). The fight itself is not hard, just the dispelling and healing at some points can get iffy. But if you get your dispelling checked and interrupts working it is not a hard boss.
After that if you have decent DPS you can try Sha. 2 heal the fight to beat enrage. But it is bit tougher then the 3 other bosses in the first wing.
If your DPS is so'n'so go Galakras, not a complicated fight, but people need to pay attention and kill the right things at the right time. 2 heal the fight.
After protectors > sha or/and galakras > take Juggernaut.
EDIT: Adding that Shamans is by no means an easy fight, even when you 3 tank it. It becomes bit annoying when you have no absorb healers in your group. Shamans demand a fairly decent HP from your raiders, so I would just take on first 6 in order you feel most comfortable with and then try out Shamans, if it's too hard try Nazgrim (our progression is at shamans atmo, so cannot comment from more then 7 first bosses). I raid 10-man, if that's any importance.