Award booking: As early as possible. Free redeposit now with AA/DL/UA/WN (non-Basic Economy), just rebook when award price drops.
Cash booking: Depends on voucher expiration policy and your ability to use voucher before expiration.

• Southwest - no expiration, book as early as possible.
• AA - expiration 1 year after voucher issued, ok to book reasonably early
• Delta - expiration 1 year after original ticket issuance, must book new trip by the expiration date, I would up to ~6 months out
• United - expiration 1 year from original ticket issuance, must commence travel by the expiration date, I won't book until 3 months before travel