The Dungeon Master's Guide covers starting wizard spells
To determine what spells are in beginning wizard's spellbook, see the Dungeon Master's Guide (1989) on Initial Wizard Spells (41).
In short, the DM picks a method to use, but a new wizard's spellbook usually contains detect magic, read magic, and about 4 other spells either that the player picks and the DM approves or that the DM picks.
The Player's Handbook Table 21: Wizard Spell Progression (43) has no impact on what spells are actually in a wizard's spellbook. That table shows only how many spells the wizard can memorize and cast of an appropriate level each day.