Is it permissible to suffice with the supplication "O Allah, make us destined for each other, and place goodness in this destiny of ours, and keep evil away from us" when intending to marry, or is it preferable to perform the Istikhara prayer?

Relationships between unrelated men and women are forbidden and must be repented from and ceased immediately. Islam does not recognize any relationship between unrelated individuals except through legal marriage, as the Prophet (peace be upon him) said: "There is nothing like marriage for two who love each other." If a person is serious, he should propose marriage, and the fiancée should cut off communication with her fiancé until the marriage contract is concluded.

It is permissible to pray for Allah to grant you marriage to him, and Allah will make good come from your supplication, either by fulfilling your request, or by averting evil, or by storing up reward for the Hereafter. This is based on the Prophet's (peace be upon him) saying: "There is no Muslim who supplicates with a supplication in which there is no sin or breaking of kinship ties, but Allah will grant him one of three things: either He will hasten his supplication for him, or He will store it for him in the Hereafter, or He will avert evil from him equivalent to it."

You must be content with Allah's decree, for Allah is All-Knowing of the reality of matters, and a person does not know the unseen. One might pray for something evil, thinking it is good, and Allah averts it from him out of His mercy, as Allah Almighty said: "And man invokes evil as he invokes good; and man is ever hasty." It is better, if this person proposes, for you to seek Allah's guidance through Istikhara.