Hi friend,

Yes, it is good to have a mental anchor to repeat peacefully (silently) during single-point meditation and to return to after you catch yourself day-dreaming. You could try watching the breath, or repeating casually (and silently) a powerful sound (“while not watching the breath”). Such a sound could be "I am" or "I'm" which is really a Western interpretation of the sound of a Sanskrit seed mantra. These sounds are sometimes considered to be meaningless, that is, they do not draw out individuality (so that’s good!). There are a limited number of bija (or seed) mantras known today. Do not use any word/sound (whether you choose you own, or are given a bija mantra), which changes the neutrality that a breathing anchor could offer.
Do not use any mantra if it moves in any direction except a change in sound (slight pronunciation change is fine), it should not be filled with meaning (how else are we going to control our ego?). It should never be: "I am"..I'm here...I'm unique...I’ll show them….etc.
It should never turn into a prayer or motivational self-talk, those are great but different.

In working towards a still mind, a very important aspect is to disregard all naturally occurring thoughts.
Part 1
Mindfulness- preparation for single-point meditation or for anytime.
One aspect of daily training is to learn to only watch your thoughts for "designated periods or circumstances". But you can do that at any time of day with eyes open, standing with a friend or while performing other activities.
Some schools would analyze these random thoughts, that is not what you're looking for now.
Do not latch on to any idea that comes up, do not give any the time of day.
Not any musical thought, any lottery number, any ideas for dinner.
Let the thought come and do not answer, let it go for this practice. This is all called mindfulness. Call it deep relaxation and also preparation for the attention you will give to your single-pointed focus: Breath, or bija matra.

Part 2- This second step can lead you deeper-Single-point meditation

Remember for this second step, your mantra should be neutral and not some of the longer ones that are bestowing graces to and from spiritual entities. Bija mantra meditation should never challenge your religious or spiritual beliefs. You repeat, you stop chatter, you go into your own silence.
Eyes closed, not driving, seated comfortably, lotus pose is not needed.
Gently repeat or watch your single-pointed focus, when you catch yourself day-dreaming, gently go back to your focal point. Do this for 15-20 minutes twice a day. Good ideas will come during these practices, but don't engage; That is also another practice, which is fine in its time.
A still mind can retool and retime your system, but the quest cannot contain a personal agenda. Remember single-point meditation is not prayer, and is not self-talk. This is the real "neutral" deal, going deep with no agenda. Helps creativity, discernment, and smiling.