Alpha, Beta, Unlimited, Revised
Considering only cards from these editions NOT appearing in fourth edition, we have here very unbalanced cards like the power nine (Moxes, Black Lotus, Time Walk, Time Twister and Ancestral Recall) and the dual lands (Taiga et al). That is, if your wallet can afford them. If, like mine, it can't, just skip these.
Fourth Edition, Fifth Edition, Sixth Edition
Even though the overall power level of these sets is low, several basic cards were introduced here, like Wrath of God, Pacifism, Armageddon, Lightning Bolt, Fireball, Earthquake, Giant Growth, Counterspell, Dark Ritual, Birds of Paradise, Howling Mine, Hypnotic Specter, etc. Others did not have such a long life and are not as known to new players, but are interesting and powerful, like Animate Dead, Ashes to Ashes, Balance, Desert Twister, Greed, Mana Flare, Mind Twist, Nevinyrral's Disk, Pestilence, Swords to Plowshares, Unstable Mutation. Worth taking a look to refresh your memory if you're an old school player, or to get to know how Magic was once, if you're new.
Seventh Edition, Eighth Edition, Ninth Edition, Tenth Edition
In these editions, the core set is designed to contain simple and general purpose reprints, so fewer interesting cards appear. These set are good to find roleplayers (cards that fill specific roles) and silver bullets (answers to specific decks/cards), and great for cubes that value simple cards. If you paid attention to the other sets, there will be no brand new cards here, but they are decent collections of playables, and a second chance to catch good cards.
Magic 2010, Magic 2011
Magic 2010 is similar to Seventh-Tenth Editions since most cards are reprints. However, the complexity level is higher and, for the first time since Alpha, new cards appear in a core set. Magic 2011 takes this even further, with less reprints and more brand new cards. The fact that core sets have no central theme makes most cards modular, so these two are great sets to find cube candidates. Some suggestions are: Safe Passage, Conundrum Sphinx, Acidic Slime, Baneslayer Angel, Doom Blade, Great Sable Stag, Master of the Wild Hunt, Sleep, Aether Adept, Ajani's Pridemate, Brittle Effigy, Crystal Ball, Fauna Shaman and the Titans.
An 85 card set in which every single colored card contains the word "artifact", meaning most cards are situational or linear. The ones that stand out were reprinted in some future core set (4th edition notably), except Mishra's Workshop.
A 78 card set which contains a few gems like Juzam Djinn, Library of Alexandria and Bazaar of Bhagdad. However, these cards will set you back quite a bit.
This one is much bigger: a 310 card set with plenty of underwhelming golden Legends and horrible cards. There is, however, a handful of interesting cards, like the World Enchantments.
Another small set (119 cards) in which all decent cards are also in 4th edition. The only exception is Maze of Ith.
Yet another small set (102 cards) with a few interesting exclusive cards, such as Hymn to Tourach and High Tide.
Among the 115 cards of Homelands, only Roots, Serrated Arrows, Wall of Kelp and Giant Oyster may offer... anything at all.
Ice Age, Alliances, Coldsnap
Ice Age has an incredibly low power level, despite being a large set. Pretty much anything worth mentioning has been reprinted in a later set. Alliances, despite being a smaller set, offers more content, such as Force of Will, the "free" cards such as Contagion and non-basic lands (Lake of the Dead, Soldevi Excavations, Thawing Glaciers, Kjeldoran Outpost). This one is worth taking a look. Coldsnap, being a much later set, is superior in power level, but with the awkward linear snow theme, it contains only a few splashy and good cards, such as Ohran Viper and Counterbalance.
Mirage, Visions, Weatherlight
Mirage in a step up from Ice Age in terms of power and card design. The power level is still low though. Some flanking creatures might be helpful, as a couple of utility scattered cards, eg. Dissipate, Grinning Totem, Dream Cache and Hammer of Bogardan. Visions follows that trend, but with superior card quality (see River Boa, Impulse, Suk'Ata Lancer, Fireblast). Weatherlight is similar to Visions, featuring Gemstone Mine, Mind Stone, Rogue Elephant and Ophidian.