The best advice for harmony is to listen to and analyse lots of Classical music and use selected phrases as models.
However, there are some conventions that are worth listing briefly that if you stick to will make your harmony more convincing:
- Use characteristic progressions at cadences (e.g. II6 V I and cadential 6/4s)
- Root progressions using falling thirds (e.g. VI to IV and I to VI) are much more common than those using rising thirds.
- I and VI are the best approach chords to II in the run up to a cadence
- All other things being equal, it is a good idea to keep a root position I on the first strong beat of a phrase
- Be wary of second inversions. They are rare except for the following:
- cadential 6/4 onto V
- second inversion chord IV alternating with chord I
- Avoid progressions using II other than as an approach chord to V. Chord IIb can also be used as an approach to a cadential 6/4.
- Don’t use III other than 1) as an approach to VI or 2) as part of a sequence between II and IV
- Chord VI in usually in root position
- Don’t use VII other than as VII6 resolving either to I or I6