We've rented villas on islands in Greece twice. I know the website you mentioned (there are quite a few others), but I don't book with them.
When they're not entire villas, we systematically book apartments or houses large enough for 3 or 4 people with a kitchen and outdoor space (or even a garden). Next may, we'll also be staying in a house on an island in the Dodecanese; I don't think it can be considered a villa, strictly speaking.
How was the booking process?
The same as for any other accommodation. Generally, villas are only rented for a period of at least 4 or 5 days, sometimes a whole week.
Were the villas as beautiful as they look online?
Yes, always. Be careful not to just look at the villa itself. There are three other important factors to consider:Location, Location and Location!
How was the customer service and overall experience?
We rent accommodations managed by private individuals, never by agencies or professionals. As is the case most of the time in Greece, the owners are always super kind and helpful. We've never had the slightest communication problem, even with people who only speak Greek.
Tip: Before leaving for Greece, we always take "typically French" souvenirs to give to the owners at the end of our stay. This is something everyone should do when planning a stay in accommodation managed by non-professionals (I mean souvenirs in general, not typically French ones).
Any hidden fees or surprises I should be aware of?
Never experienced any.
Note, however, that the tourist tax (Climate Resilience Tax) may be charged separately from the rental price. find out beforehand because this tax will be quite significant from 2025:
Villas: €15 per night and other holiday homes: €8 per night (under 80 sq.m.) and €15 per night (80 sq.m. and above)
.. if you have any general tips for renting villas in Greece, I’m all
ears.
Personal method:
1/ Weeks of research on Airbnb, Booking, but especially on local websites and Google Maps.
2/ Save wish lists with 10 to 15 possibilities without being too selective (I use Google My Maps to save them), then eliminate them gradually until 3 or 4 remain.
Examples of places where we have rented houses or villas:
In Paros:
https://villavanta.com/
In Serifos:
https://www.airbnb.com/rooms/13042422?
In Kythira:
https://www.airbnb.fr/rooms/29581540