The nearest airport is Nice. Transavia and KLM offer reasonable rates. You may rent a car at the airport. You get from there to Olivetta in about three quarters of an hour. If you don’t rent a car and nobody else is picking you up, you have to opt for public transportation. In that case you either take the rapid bus to Nice Central Station (tickets are for sale at the airport), or you walk in about 15 minutes to nearby train station Nice-St. Augustin and take the train to Nice Central Station; in either case you board there for the train to Ventimiglia. Five times a day a bus departs from the Ventimiglia city center (Via Cavour) to Olivetta (this takes about 20 minutes). Our house is on walking distance from there (2 km).
There are various routes. Some people think that the route Paris -> Lyon -> Nice over the Autoroute du soleil is fastest. Others insist on the route over Germany and Switzerland via the left bank of the Rhine -> Basel -> the Great St Bernard-tunnel -> Turin -> Cuneo. Again others prefer to take, from Basel onward, the St Gotthard tunnel in the direction of Milan, then Genua and from there through Ventimiglia to Olivetta / San Michele. Our own best experiences are with the route through the Mont Blanc tunnel.
Using the TGV and the Thalys you may reach Ventimiglia in a day. It is also possible to take a night train from Paris.
The cheapest way to get to Ventimiglia is by bus from Antwerp to Nice.