As far as I know, most verse of the heroic alliterative tradition was written in a four beat line. Alliteration propelled the rhythm.
Our current notions of meter are not really relevant to scansion of OE or Old Norse. Quite a few scholars specialize in the arcana of OE meter, but they must work largely from inference, and they argue fiercely about their guesses. I feel that many of them are too keen to apply modern ideas of meter and semantics to an inappropriate context.
In the equation xxxy, both x and y may have any value (i.e. be any consonant, or even, sometimes, a vowel). It is not desirable to repeat values in adjacent lines, although, as I mentioned earlier, Tim and I sometimes did so in the Beowulf. Occasionally we let the y consonant in one line take the x value in the next. That's what I meant when I referred to "bridging across lines." In such cases, the succeeding line would usually be an xxyy or xyxy, in order to avoid too many consecutive alliterations.
The scops of antiquity were much stricter. OE was an inflected language, with more unstressed syllables than modern English. Three or even four unstressed or weakly stressed syllables might separate alliterating stresses. In the tighter format of Modern English, it is easy for alliteration to sound silly. That may be the principal reason why it fell from favor.
I am unaware of any rules or even general principles either favoring or restricting proximity of plosives or other subtypes of sound. OE did have markedly high frequency of certain initial consonants in its vocabulary. The pattern is different in modern English, which ingested a lot of new sounds with Norman French. Obviously such built-in biases have some effect on alliterative verse.
I have a more thorough discussion of these matters in the essays I wrote to accompany the Beowulf translation. If you'd like to PM me your mailing address, I'll send you hard copy.
A.S.
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