You're going to fall in love with whichever Island you go too. There's just something so magical about Greece.
I'd be lead by the flights. The more popular islands have the most choices and you can try to avoid the killer late night home flights. Corfu, Zante, Rhodes, Crete are the most accessible and offer the most chance of a budget bargain. But chose resorts wisely as there are some crappy mass tourist places to avoid. Crete is almost like a country in it's own right and is packed full of culture. Around Elounda is stunning and has some wonderful hotels.
If you're going low season the Ionians can get rain- they are lovely and green though so again Crete, Rhodes or Kos which are further East will have less risk of poor weather.
Mykonos is a great starting point to Island hop- and full of beautiful people- but much more expensive than other islands. Santorini is one of the most spectacular places on earth- but you pay for those views- and it gets heaving with Cruise crowds.
Paros is super chic and pretty - Nauossa is totally stunning and full of glamourous yachties- but there's no airport so its a faff on the ferry - worth it. Naxos is also airport free- but this means its not reliant on tourists- its a big interesting island that felt the most uncommercial to us. Good beaches too.
Other fave place was Fiskado on Kefalonia. Arguably the most beautiful island - amazing in spring and slightly quieter than Zante and Corfu close by.
We've never had a disappointing Greek island holiday in 30 years of visiting but Zante, Kos and Lesbos were a little less amazing......
Overall though there's one island we keep going back to and that's Skiathos. There's just something other wordly about the light and the sparkly blue of the sea. Its small enough to feel like an island- but sophisticated enough to have great bars and restaurants. Plus beaches that look like the Carribean (most are sandy which is rare for lots of the islands).
Sorry for the long post- we were booking our June trip to Symi (new island for us) last night so everything is fresh in my mind xx