To get the best out of this collection it is important to get away from two disastrous conventions. Both derive ultimately from the 1st edition of Hymns Ancient and Modern.
The first is the notion that there is a right tune for each psalm. With a few examples which are mentioned in the headnotes in the collection, there is not. The traditional approach was always much more fluid as to which psalm went with which tune. It is the role of the organist or the band to choose one. The same psalm can have a quite different feel, suitable for a different occasion, simply by being sung to a different tune. This is why the Scottish Psalter used to be produced in stable door format. It was designed to enable one to mix and match psalms with tunes in the right metre and mode.
So although each psalm has a tune, you are free and encouraged to use any tune that fits, or even to write new ones. I would like to hear what tunes people might have tried and whether they fitted well or badly.
The second is that traditional (i.e. pre 1850) hymn tunes are more flexible than we realise. The first compilers of Ancient and Modern had very particular ideas about the sorts of music they did not like. They forced a lot of tunes into a very plodding style, because they thought it was more dignified and so more holy. Before that, they were more likely to be sung with the addition of passing notes and other forms of ornamentation. The tune to Amazing Grace would never have taken wing as a popular tune if it had been kept corsetted in the plonking style of the average late C19 hymn book. Many other tunes have much more to offer if they too were liberated from those constraints.
The one thing musicians do need to bear in mind, is that tunes for these traditional metres tend to be built round melody rather than rhythm. That though also applies to much popular music prior to the change in the scope for electronic amplification in the late 1960s. So these tunes offer more scope for a scratch band which includes melodic instruments, flutes, fiddles, clarinets, saxophone, etc rather than an exclusively beat band built solely round guitars and percussion.
For those that can manage it, they often work particularly well to harmonic arrangements. Many of these tunes derive from a time when a different instrument played each line, and the congregation followed the instrument that went with their voice.