With less than $20 for a year, it will be hard to really meet all of your requirements:
- Economic and reliable hosting
- Access to support
- Lot of bandwidth and support for PHP (so that I can run scripts for PHPBB etc.,)
- Good response and uptime.
Maybe you should increase your budget a little to really get what you need
I agree that 24/7 support is important as you may need it for urgent case and it is true that you should test them first before you sign up