Is it permissible to make the supplication, "Oh Allah, grant me success, guide me, and destine for me what You love and are pleased with most, and what is best for my Hereafter in every word, deed, and everything," instead of a specific supplication, because Allah knows best what is good for His servant?

The best approach to supplication is to use comprehensive phrases (Jawami' al-Kalim), such as the supplication mentioned in the question. It is also permissible to supplicate for individual needs as long as they do not involve sin, for the Messenger of Allah (peace and blessings be upon him) said: "Let one of you ask his Lord for all his needs, even if it is for the shoelace of his sandal when it breaks." The Prophet (peace and blessings be upon him) preferred comprehensive supplications. An example of this is what he taught Aisha (may Allah be pleased with her): "O Allah, I ask You for all good, sooner and later, what I know of it and what I do not know. And I seek refuge in You from all evil, sooner and later, what I know of it and what I do not know. O Allah, I ask You for Paradise and what brings one closer to it of word or deed. And I seek refuge in You from Hellfire and what brings one closer to it of word or deed. O Allah, I ask You for what Muhammad (peace and blessings be upon him) asked You for, and I seek refuge in You from what Muhammad (peace and blessings be upon him) sought refuge in You from. O Allah, whatever decree You have decreed for me, make its outcome guidance for me." And most of his (peace and blessings be upon him) supplication was: "O Allah, our Lord, grant us good in this world and good in the Hereafter, and protect us from the torment of the Fire."