I think a better phrase than ‘worship’ could be something like ‘love, reverance, and awe’ – which to a significant extent is what worship means, anyway, but makes it more fresh and relevant to a typical, contemporary English speaker’s ear.
Etymologically, ‘worship’ seems to come from Old English ‘condition of being worthy’, and to worship God is to recognize something of value. This makes some sense of the first commandment, to have no gods before God. I.e., to not value other things (such as money or power) more than you value your relationship with God. This makes sense if God exists, because God is good for you, according to Christianity.
You can think about it like this: things are potential goods. They are tools that, to create good in one’s life, require skillful use. Money, for example, can do great good, but it can also damage someone. Being aligned with God is like being aligned with a master craftsman, who can then guide you in using (or disregarding) those other potential goods to add to your life (and your society’s).
The Christian God is the god of a kind of love (which is captured by the idea of willing the good of the other for the sake of the other), and so the major decision in Christianity is to love God back, and then let that love from and to God flow through one to other aspects of the universe (other people, primarily, but also the environment and ultimately the entire universe, which according to Christianity it is our role to steward, guided by a divine wisdom, i.e., the living Christ).
To revere something flows fairly simply from valuing it. You can revere your parent, for example, which is to say you care about them and want to honour them.
Awe flows naturally from the nature of God – when you realize He has coordinated some outcome that seems unfathomable, say, this naturally leads to awe. If you view the starry sky, and believe God is tied up in the creation of it, this naturally leads to awe. And so on.
Added to love, reverence, and awe could be ‘speaking’ and ‘listening’ (both understood spiritually), which seems like a central aspect of understanding God (i.e., guidance, discernment, and so on).
These four aspects are associated with the Christian idea of God as a spiritual Father, or ‘Abba’.
So, if the word ‘worship’ gets in the way of building a relationship with God, you can instead think of love, reverence, awe, and speaking-listening. More simply, instead of ‘worshipping’ you can say ‘valuing’.