Small MS Access Application - MySQL backend - Best Host?

Beware "free" anything, including remotely hosted database services. You get what you pay for in most things; this is one area where you might want to think carefully about that. This is not a private photo collection. This is your organization's business data. How long would you be down if this "free" remotely hosted database service doesn't work out?

I'm not saying it's impossible, but I am saying that your employer might not be all that excited about moving their data (and it is the company's data, after all) into the cloud this way.

Make sure your employer knows exactly what you are doing with their data.

If you can't afford a small fee for a monthly remotely hosted MySQL database, then I'd have to wonder if the need is really there.

Another consideration, which I have personally encountered, is whether a "free" web hosting service is going to let you connect your Access front ends remotely to the MySQL on their site. They are, I believe, mostly aimed at supporting web sites. If you do go there, look before you leap.