Perhaps you want to start a daily prayer, or at least regular prayer discipline and you don't know where to start. (This also applys to small groups, say UUCF chapters.) The available Anglican and Catholic books are written with a certain amount of in-knowledge that is difficult to acquire. And perhaps, if you are a Universalist or Unitarian (or Unitarian Universalist) want to start with something homegrown and handy. I can help. Go to a certain hymnal.
OK, the old red hymnal, Hymns of the Spirit is neither perfect nor in print, but if you are in a town with a Unitarian or Universalist church founded before (say) 1950, you might be able to beg or borrow one if you ask nicely. (Don't steal.) Or perhaps you have one. Or you can go to Ebay. (Don't pay more than $10 in any case. They're not that rare.)
"Ideally" daily prayer for non-monastics runs morning and evening. And ideally I would be making a lot more money. In both cases: start with what you have and can manage. For the sake of arguement, try evening prayer. (Which will be more likely for a group.)
The "second order of service" is a good evening prayer service: its themes are lightness in the dark, here, the literal darkness of the (coming) night.
If you're reading your prayers along, start with a couple of sentences, then the exhortation (in which case the "we" is the Church Universal) , the invocation, skipping to the Lord's Prayer, and then skipping to the prayers, using at least the first and last one.
If this is an act of pure praise, Bible lessons that make you think and reflect are out of place. (Ain't ya' tired by evening?) If you want to study scripture, alone or in a group, do that after your prayers. If you want a small portion of scripture to meditate on, that's another matter and can be re-inserted at "first lesson."
Likewise, at "responsive reading" there really should be a psalm or Bible song, which also is a vehicle for praise, prayer, and meditation. I'm not thilled with the responsive reading selection in this hymnal, but selections 5, 23, and 69 include traditional fragments appropriate for evenings. Don't read them too fast.
You might want some extra prayers after those mentioned above see pp. 136-147 and the "communion prayer" (p. 151) from the shorter Communion service.
As for the matter of gender and language. Yeah, it isn't gender-inclusive, and I've come to the point htat sometimes I want to change something, and other times I'll let it stand. If you're praying alone, do what you will, and be generous to feelings about tradition as well as sex equity.
But try the service as-is a few times before makeing any changes. Trust me. After a few times you'll have a better sence of why things belong where they do, and you'll make better choices in your alterations, if you make any.