I've been a Maiden fan for a long time, I'll give you a brief opinion of each album.
1980: Iron Maiden ; Maiden at their rawest , the production is pretty horrible but , at this point, I wouldn't want to hear this album any other way. The songs are all strong on this one. This album kind of has a punk vibe but with better guitar work than most punk albums at the time.
1981: Killers; Once again (as far as I'm concerned), there is no filler on this album and the musicianship seems to be up a notch from their debut, especially Clive Burr's drumming. Martin Birch produced this one and you can hear the leap in quality . This album is straight ahead metal with much less of the punk vibe of IM's debut. Once again, Clive's drumming on this album is amazing and I highly recommend finding youtube clips of Maiden live from this period. Try searching 'Maiden Milan 81' and 'Maiden Bremen 81'.
1982: The Number of the Beast; Maiden loses Di'anno's gruff streetwise sounding voice and gain Dickinson's mainic screams and banshee wails. To me the music kind of loses the manic speed of millitary tightness of Killers but gains a looser more bluesy feel. I guess one might consider 'Invaders 'a filler track but who opens an album with filler? I think it was more of a misjudgement by the band. Sometimes I think 'side a' was actually meant to be 'side b' but the record company screwed it up at pressing. That would explain the running order.
1983: Piece of Mind ; Maiden loses Clive's incredible feel and speedy cymbal bashing and gain Nicko's more deliberate and trained drumming. The music takes on an even less manic feel and you get an almost progressive rock version of Maiden. Even the songs you know are filler on this album are classics. Sun and Steel and Quest for Fire (although for its unintentional cheesiness), are never skipped when I play this album. Also on this album , the guitar work seems a little more subdued then previous releases...almost a tad more Sabbathy , especially on the song 'Revelations'.
1984: Powerslave; A great mix of fast scorchers and epic material. Some things start to get a little overblown and ponderous on this album but that kind of just adds to the epic PowerMetal feel of this album. Once again, there is filler on this album but somehow those songs have grown to be classics as well.
1985: Live After Death; This was my first Maiden album and the beginning of my love affair with this band. This is simply Maiden , but a fatser, louder Maiden . You get to hear most of the classics the band had up until this point so what is not to like? Bruce's voice may be a little too raspy for some though...
1986: Somehwere in Time; It's like an old car with a new paint job. Somehow Maiden manage to use guitar synths and bass synths and not sound like Genesis or Def Leppard. Some songs on this album like ' Sea of Madness' would actually be less heavy without the synths. I also think Maiden's musicianship is top notch on this album, especially the guitar work. You can definately hear Adrian Smith's influence all over this album.
1988: SSoaSS; Maiden actually take off a year and come back refreshed with possibly their best album ever. To me, this album doesn't have a single second of filler and is the most realised Maiden album of them all. This is Maiden at its progressive rock zenith. I would suggest downloading the song Moonchild and playing it a full volume to get psyched for this masterpiece.
Those are essential. After that i would get Brave New World then AMOLAD and then Dance of Death. The remainder of their studio work is very hit and miss.