What is the ruling on saying "I will do such and such, and the rest is up to Allah," and does it indicate a lack of reliance on Allah?

Reliance on Allah is required, and scholars define it as taking the necessary means while realizing that they have no effect except by Allah's permission, and that the true reliance for the success of a task is on Allah alone. This does not prevent you from doing what you can in terms of taking means. For, exerting effort does not contradict reliance if you are dependent on Allah. This is what is indicated by the hadith "Tie it and rely," and the Prophet's (peace be upon him) planning during the Hijra and his wearing of armor in Uhud. So, whoever exerts his utmost effort and relies on Allah, his action is not considered contrary to reliance. As for relying solely on oneself, it is contrary to reliance. And the statement "The rest is up to Allah" means that actual success is not the responsibility of the person, so there is no harm in it.