Psalm 101 is a David psalm, but not really. It is perhaps a psalm for David, or looking forward to a better David, rather than a psalm about David (one key is Yhwh's house (v2,7) was not constructed under David but his son, Solomon). It is the first David psalm for a while (not since Ps 86), and, with Psalm 103, is one of only two "David psalms" in Book IV.
It's an interesting psalm, which shifts quite a bit after the first four verses. That is, in the first four verses, each clause contains a verb, and although they are all related, any clause could stand on its own.
1 Of steadfast love and justice shall I sing
you, Yhwh, shall I praise
2 I will closely attend to the blameless path
when will you come to me?
I will walk with integrity of heart within your house
3 I will not set before my eyes worthless words
the deeds of deviants I hate
it will not cling to me
4 the heart of the crooked will turn from me
no evil shall I know
In the first half of this psalm we find mostly 1st person yiqtols, the "I will ..." verbs; only "I hate" is a qatal among the 1st person verbs. Nonetheless, the distribution of the verb is either at the front or the back of the clause. It seems more regular (to my ear) to have it at the front, while when it's at the back (v1a,b; 4b) it seems to highlight what precedes it (steadfast love and justice, Yhwh, no evil).
The second half of the psalm, from 5-8, each line depends on two clauses to make sense, as follows:
5 the one slandering in secret their neighbour
this one I will silence
the haughty eyed and arrogant hearted
this one I will not endure6 My eyes [will be] upon the faithful of the land
in order [that they] might dwell with me
the one walking in blameless paths
this one will minister to me.7 They will not dwell in the midst of my house,
whoever does deceit.
whoever speaks falsely
will not be be established before my eyes.8 By morning I will destroy
all the wicked of the land
in order to cut off from the city of Yhwh
all doers of iniquity
As you can see, you need both clauses to say something. Who will not dwell in my house? Whoever does deceit. And so on. Verse 8 is really the only verse which seems to be one thought over four clauses. 5-7 however are all good examples of synonymous parallelism, where both halves say essentially the same thing.
There might be some overarching structure, with Yhwh only in the first and last verses, and your house // my house (v2, 7). There's also a contrast between the "faithful of the land" who will dwell there, (v6) and the "wicked of the land" who will be cut off (v8).
As a whole, this psalm feels unfinished, with no development. If anything, it feels like a downwards spiral, from praising to destruction, from calling on Yhwh to act at the beginning, while at the end committing to enact human judgement. I would almost prefer to read this psalm in the reverse order, where we move from human action to trusting and praising Yhwh alone.
So I'm not really sure what to do with this psalm. It could be I'm tired after a week of travel and sickness and classes I can't see why anyone would have this psalm as their favourite.
As an exodus psalm, this almost feels like Moses speaking to the Israelites after they have been caught in their idolatry and no more will he put up with sinfulness among the people. Only those who match their words (1-2b) with their actions (2c-4) will be those who may come into Yhwh's promised rest.
