I'm trying to figure out how to say “it would be my pleasure”, is it “ce serait mon plaisir” or “il serait mon plaisir” or is it neither? If so, what is the French equivalent?
a3nm's suggestion is idiomatic at the present but less used at the conditional.
user16924 gave a better hint with avec so the closer translation would be:
Ce serait avec plaisir.
Other possibilities might be:
J'en serais ravi.
Je serais ravi de...
Je serais enchanté de...
Vous m'en verriez ravi.
is it 'ce serait mon plaisir' or 'il serait mon plaisir' or is it neither?
Neither is used, although it would be grammatically correct (at least the first one; the second one sounds incomplete).
a3nm's answer is correct. You could also use "avec plaisir".
A common phrase (a bit formal, often used somewhat jokingly) for this is "Tout le plaisir est pour moi", i.e., literally, "All the pleasure is mine". In your case, "Tout le plaisir serait pour moi", i.e., "All the pleasure would be mine".
That depends upon the context. For instance
"it would be my pleasure to meet you" --> "ce serait un plaisir de vous rencontrer". But if I am sure to meet him, I would say "ce sera un plaisir de vous rencontrer". Anyway, "my" must be dropped.
Another instance: "it would be my pleasure to eat with my colleagues". Literally no French would use "ce serait un plaisir de manger avec mes collègues", he would rather say: "j'aimerais manger avec mes collègues" ou "j'aurais (grand) plaisir à manger avec mes collègues".
The others has already provided great answers. Just as a side remark. linguee.fr may be quite useful for such staff. So, for instance, by typing "would be my pleasure"...
...one sees various possibilities; some of which have already been pointed out. Among these possibilities one encounters:
It would be my pleasure. Je le ferai avec plaisir.
It would be my pleasure to share these results with you in a few months. Je serai heureux de vous en présenter les résultats dans quelques mois.
The point is that sometimes it is not possible to have an one to one correspondance and word by word translation from English to French and vice versa and there are various French structures that may interprete a single English one and vice versa.