What are the differences in meaning between the prefix of the letter ל (lamed), when different vowels are used [i.e. לַ (patach), לָ (kumatz) and לְ (shva)]? What about variants of the usage of the letter ו (vav) as a prefix?
Regarding vav, see msh210's answer here.
Regarding lamed, Wikipedia has a nice article discussing prefixes in Hebrew. A short summary follows, but see there for all the details:
Lamed meaning 'to' normally takes a sheva, although there are exceptions for cases when the next letter of the word has a specific vowel (e.g. before a sheva the lamed instead takes a chirik (e.g. לִירוּשָׁלִַם)).
If the meaning is 'to the' one might have expected to see a lamed followed by a heh ha-yedi'ah. What actually happens is that the heh falls away and the lamed takes the vowel that would have appeared under the heh (normally a patach (e.g. לַמָּקוֹם) but, for instance, before an 'ayin a kamatz (e.g. לָעִיר)).