I never used Gamecentre but I wondered if it can be set up to list peoples words and the word explanations and the people post them themselves?
You can use Gamecenter as a login to track users but you'd still need to save the word data on a server somewhere.
There are sites which offer free sql databases. Most hosting packages offer sql databases with their package. I guess it defines what you call expensive. I would say cheap unless you become insanely popular and need to scale up. However if you are just doing a small number of operations you will be fine even with a large userbase.
Severs from Digital Ocean starts from $5/month and they are giving $10 promo codes right now.. https://twitter.com/digitalocean/status/473174289449897984/photo/1 I'm not affiliated with them in any ways I recently did some search on cheap server providers and Digital Ocean and Linode seems good. But I ended up using my old MacBook as a server (until I need to scale..)
You could use a small virtual server with pay as you go rates so you don't need to get more server than you need. Amazon Web Services offers a hosted virtual server... you might even qualify to stay in their 'free' tier.
