>4. make a collection of views on the log table...

Jan,
forget option 4 - views are basically queries on underlying table(s) and
cannot be used for increasing speed.

I'm not certain if logging to a table is a good idea at all, but others
will be able to tell you more about that and about your other three
options. But if you do, I do not understand why you don't have any
additional indexes besides the primary key. Have you tried having an index
on (logtype, PrimaryKey)? Indexes should be close to unique, so having an
index on logtype alone could lead to performance degradation (though I'm
not certain if this matters for inserts or only affects deletes), so adding
the PK to the index can be quite useful.

HTH,
Set