How should a Muslim adhere to istighfar (seeking forgiveness) to attain what is mentioned in the hadith: "Whoever adheres to istighfar, Allah will make for him a way out of every difficulty and a relief from every worry, and will provide for him from where he does not expect"? And is it better to engage in istighfar or to send blessings upon the Prophet (peace be upon him)?

The hadith mentioned in the question has a weak chain of transmission, but its meaning is sound. "To be assiduous" (lazima) in seeking forgiveness means "to do it often" or "to persevere" in it. Seeking forgiveness should be accompanied by repentance and remorse, and the established, legally prescribed formulas should be used. It is preferable for a Muslim to combine seeking forgiveness with sending blessings upon the Prophet, peace be upon him.

Seeking forgiveness is more likely to be recited frequently in every gathering for two reasons: 1. The abundance of hadiths detailing its virtues. 2. The frequency with which the Prophet, peace be upon him, performed it.

Some scholars consider sending blessings upon the Prophet to be more comprehensive and more virtuous, especially if the hadith of Ubayy ibn Ka'b is authentic, although there is some discussion regarding its chain of transmission.

Summary of the Matter: 1. Seeking forgiveness should be prioritized after committing a sin. 2. Seeking forgiveness is more likely to be recited frequently. 3. Whoever deems the hadith of Ubayy ibn Ka'b to be authentic has a strong argument for prioritizing sending blessings upon the Prophet. 4. It is best for a Muslim to combine both forms of remembrance to benefit from their diverse virtues.