While the most "true" way would be to play the whole AC series from start to beginning, not everyone would be willing to do such a marathon, though by doing so you'll be a witness how from each game to each game Armored Core has evolved.
From older ones, it's "
Master of Arena" and "
Silent Line" which are considered the best in franchise, and from newer ones it's "
For Answer" or
"Verdict Day" depending on reasons.
I haven't played all games in series, but can share what i know:
(PS1) Armored Core - the game that started it all. While some mech designs might be simple here, and you could have a problem with vertical camera (ps1 controls, yeah), it was a very solid start. The most thing that impressesed me though is actual control of mech itself - so smooth and so versatile.
(PS1) Project Phantasma - some people liked it, some hated - controversial opinions.
(PS1) Master of Arena - arena mode was the meat of game, though you had campaign too. And here it introduced ability to train AI of npc mechas.
(PS2) AC2 - rushed release for Playstation 2 debut, clunky in many ways.
(PS2) Another Age - better, and some people seem to have fond memories of it.
(PS2) AC3 - that's where series returned to it's quality. Different new additions: 4-player mp, detachable parts, dual wield, etc. Also, rebalancing of game and much better game engine than in AC2.
(PS2) Silent Line - favourite by many AC fans. And AI training is back and improved.
(PS2) Nexus - it has 2 discs, on 1st disc you have new missions, on 2nd you have remakes of some ps1 ac's missions. As usual, some changes in mechanics and even control scheme (now you can use gamepad like in fps/tps games if you want).
(PS2) Formula Front - strange release. It's like football manager sim - but with mechas. Just more experiments with AI customization.
(PS2) Ninebreaker - another strange release, hated by many. It uses AC Nexus' engine, and it has 150 "training missions" and arena. Yeah, all to prove that you can call yourself a "ninebreaker".
(PS2) Last Raven - in my opinion, it's most badass game in series
anyway, well. It has campaign with some twists (as usual, choosing missions in non-linear, so depending on your choices you end up supporting this or that clan and different mission objectives and final bosses), it has arena mode and, of course, multiplayer. Some say LR is the definitive one of you want to play some versus from older ACs. Also, a game can give some nice challenge (especially if you don't import parts from ac3/sl/nexus)
As usual, some changes in mechanics - breaking of parts, rebalanced heat, a bit different physics (master your movement!), more comfortable garage (and you can tune parts here too). Also, From Software worked nice on enemy AI here - the thing it, depending on your current mecha setup, enemies will change their behaviour to counter threats from you.
(PS3/X360) AC4 - new direction of series, yeah.
(PS3/X360) For Answer - really really really epic game, especially because of Arms Fortress. Also has interesting designs provided by different mecha artists.
(PS3/X360) AC5 - huge disappointment for many many players, both fans and non-fans. AC changed direction again - from ultra fast AC4/fA to much slower ?tactical? approach and aimed at online multiplayer.
(PS3/X360) Verdict Day - opinions are controversial, for some it's best game in series, for some it's "same shit as ac5". Anyway it improves many flaws of AC5. As for "campaign or multiplayer" - well, online multiplayer was more important thing in this game as From Software used all experience they had with Chromehounds (if you may remember) and put it here. THOUGH, single player might be enjoyable too espacially if you like going for S rank.
What bothers me is uncertain future of series. From is too busy making Souls-like games to earn $$$.
Ah, and to end my post just two videos i found (note: author's of videos uses another music tracks):
1)
https://www.youtube.com/watch?v=9GK9uzqsW0Q impressive video of sense of speed in for Answer
2)
https://youtu.be/H6DZ72ZyvrA recording of match in some aclr tournament from ACU forums. more videos on channel. not sure if they use psp version with emulator and tunneling software as i recall ps2 version has slightly better gfx
