I think the best way to understand the elf favored class of wizard is to think that elves often mix wizard with whatever else they do--elves will often be rogue/wizards, fighter/wizards (bladesingers or arcane archers), cleric/wizards, etc. As others have said, elves don't make particularly good single classed wizards.
So, here are a few basic strategies for playing wizards:
1. The ray specialist
Focus: Ray spells without saves
Key feats: Point Blank Shot, Precise Shot, Empower Spell, Spell Penetration, Greater Spell Penetration, Quicken Spell
Key spells: 1: Ray of Enfeeblement, Lesser energy orb (Mini HB); 2. Scorching Ray; 3. Empowered Ray of Enfeeblement, Ray of Exhaustion; 4: Empowered Scorching Ray, Enervation; 5: Quickened Ray of Enfeeblement, Quickened Lesser Energy Orb, 6: Disintegrate, Empowered Enervation, Quickened Scorching Ray; 7th: Quickened, Empowered Ray of Enfeeblement, Quickened Ray of Exhaustion; 8th: Quickened Enervation, Empowered Disintegrate, Polar Ray; 9th: Energy Drain
Strengths: With an emphasis on no-save spells, Int is less essential than for other builds--a 15 int would be sufficient.
2. Blaster
Key feats: Spell Focus and Greater Spell Focus: Evocation, Spell Penetration, Greater Spell Penetration, Quicken Spell
Key spells: 1: Magic Missile, 2: Scorching Ray; 3: Fireball; 4: Ice Storm; 5: Empowered Fireball; 6: Chain Lighning, Otiluke's Freezing Sphere; 7: Prismatic Spray; 8: Horrid Wilting; 9: Meteor Swarm
Strengths: Most things are susceptible to some kind of damage
Weaknesses: Most spells are save dependent and are subject to energy resistances. This character needs as high an int as possible in order to crank the save DCs.
3. Battlefield control mage
Key feats: None
Key spells: 1: Grease, Obscuring Mist; 2: Fog Cloud; 3: Sleet Storm, Slow; 4: Otiluke's Resilient Sphere, Solid Fog, Evard's Black Tentacles, Wall of Fire/Ice; 5: Wall of Force, Cloudkill; 6: Acid Fog; 7: Bigby's Grasping Hand; 8: ForceCage, Prismatic Wall, etc.
Strengths: Most of these spells don't have saves and aren't subject to SR. Consequently, you can get by with lower int and without spell penetration, etc.
Weaknesses: This style of wizard requires a keen tactical player. It also doesn't deal much damage by itself and requires other players to dish out the damage. In a group of gloryhounds, or tactical incompetents, this can be ineffective. High CR outsiders also have ways of evading most of the effects of this strategy.
4. Save of Die/Screw
Key Feats: Spell Penetration and Greater Spell Penetration; Spell Focus is also helpful (usual schools: necromancy, enchantment, Illusion, or Transmutation)
key spells: Ray of Enfeeblement, Sleep, Color Spray, Cause Fear; 2-Scare, Tasha's Hideous Laughter, Blindness/Deafness, touch of idiocy; 3-Suggestion, Slow, Hold Person; 4-Confusion, Charm Monster, Otiluke's Resilient Sphere, Phantasmal Killer; 5-Dominate Person, Hold Monster, Magic Jar; 6- Flesh to Stone, Disintegrate; 7-Finger of Death; 8- Power Word: Stun; 9-Wierd, Wail of the Banshee
Strengths: Often takes foes out of the fight instantly
Weaknesses: Subject to both saves and SR; requires as high an int as possible; often does nothing on a successful save.
5. Party buff
Key Feats: Extend Spell
Key spells: 1- Enlarge Person, Mage Armor, Magic Weapon; 2-Bull's Strength, Cat's Grace, etc., Resist Energy; 3- Haste, Heroism, Displacement, Magic Circle vs. Evil, Flame Arrow, Keen Edge; 4-Polymorph, Greater Invisibility, Stoneskin; 5-; 6-Greater Heroism, Fires of Purity (Complete Divine); 7-Protection from spells; 8-Mind Blank
Strengths: no saves, no spell resistance, no need for high int, always works
Weaknesses: Depends upon the tactical abilities of others, sometimes you need the offense this strategy does not provide.
6. Utility:
Key feats: none
Key spells: 1-Unseen Servant, Identify; 2-Knock, Rope Trick, See Invisibility; 3-Arcane Sight, 4- Leomund's Secure Shelter, Mage Eye, Scrying, Dimension Door; 5-Prying Eyes, Teleport; 6- Analyze Dweomer, Legend Lore; 7-Mordenkeinen's Magnificent Mansion, Greater Teleport, etc.
Strengths: No saves (generally), no SR, helps control the party's environment and inform their approach to it.
Weaknesses: doesn't damage foes or directly help the party; once your in combat, it's often too late to use it.
Most successful wizards have the spells and feats to combine one or two of these. For instance, a wizard might focus on ray spells and battlefield control spells. He uses battlefield control to deal with large groups of enemies and ray spells to deal with single enemies or enemies with lots of mobility. Another wizard might focus on battlefield control and save or die/screw spells. He uses battlefield control to limit groups of foes and foes with high SR and save or die spells to target individual foes. Yet another wizard might focus on blasting and keep party buffing as a backup strategy. Such a wizard would blast first and buff his party when foes proved resistant to blasting (good saves, energy resistances, etc).
Wizards will generally focus on one or two of these strategies and keep a few other avenues open should they need them and have time to reprepare spells. Some will even use one strategy through the low levels and develop new strategies at high levels. For instance, ray spells are very effective early but good save or screw/die spells start to come later. So a wizard might start off with ray spells as his bread and butter and branch out later. Wizards are also better able to deal with utility spells that need casting from time to time but aren't spells you would cast every day. Their greater variety of spells known makes them more able to choose spells that they will only use occasionally. Wizards are also more effective blasters and ray attack specialists in the short term because they are more easily able to use quicken spell than sorcerors--thus enabling them to put out their firepower more quickly.
Sorcerors are a bit more limited in their ability to switch between strategies and to develop new strategies at high levels. They also have fewer feats which keeps them from being quite as versatile as wizards. Their extra spells per day, however, can give them more endurance in the ray attack specialist, blaster, save or die/screw, and certain party buffing roles. A sorceror can cast Heroism on everyone in the party before entering the dungeon, for instance. A wizard would have trouble stretching his spell slots to do that.
