The Language Construction Kit explains that sound changes are usually regular, and provides a few examples. Advanced Language Construction adds information on where in a society sound changes tend to start, how they tend to spread through society, and how morphosyntax tends to change over time. But what kinds of sound changes are generally how common? Are there any rules about that? What kinds of sound changes tend to happen together with what other kinds of sound changes? When sounds change, are there usually any rules about that aside from “Sound A, under B conditions, becomes Sound C”? And what resources are there on all these topics?
First, the easy part: the LCK has a list of common sound changes (p. 169, in edition 1.2). You won’t go wrong with any of them. In particular, the ones identified as lenitions occur just about all over.
If you’re going to be doing this a lot, you might look at another book on historical linguistics— I like Theodora Bynon’s or R.L. Trask’s books, both called Historical Linguistics. If those are not readily available, any intro from a university press is probably good.
The old ZBB has an enormous thread full of sound changes. It’s tedious to browse but it does have ideas from around the world.
You can also, informally, look through my numbers list, especially in families with a proto-language listed. You can see a lot of sound changes at a glance. (Admittedly many are obscured by different romanizations.)
I don’t know if anyone has catalogued which are the commonest sound changes, but I’d say not to worry about it too much. Choose sound changes you like, and which twist the source words in an interesting way. You can’t really criticize a sound change for being weird, especially if at least one natlang does it! Weird things do happen in language.
Try to think about changes affecting categories of sounds. E.g. it’s better to have a change that affects all voiced consonants between vowels, rather than one that affects just /d/, or different ones for each consonant. Especially with lenitions, or simplifications of consonant clusters, your people are likely to approach similar sounds in similar ways.
With vowels, sometimes you can build a chain of changes, such as the Great Vowel Shift in English. Think of it as one vowel moving into another’s territory; that one then moves to escape it, triggering more changes.
Adjoining languages may share sound changes, even if they’re unrelated. E.g. it’s presumably not entirely coincidence that French and German, unlike most of their neighbors, developed ü ö and the uvular R. Vietnamese has developed tone, like Chinese, though most other Austro-Asiatic languages have not.
Finally, your next question is probably going to be “How do I know when I’m done?” My answer is roughly “When your sound changes affect every word in your sample.” You can also try to impressionistically compare your family to natlangs of a similar time depth. E.g. Latin vs. French is a good example of 2000 years of change; Old vs. Modern German is a good example of 1000 years. (Or look at written vs. spoken French— written French is a pretty good phonemic representation of the 12th century spoken language.)