I'm looking to move away from my current Host.
Currently I'm paying $20US/mo for the following:
30gb disk space
1000gb bandwidth/mo
I'd like to find a shared host for a similar price with established fast and helpful support who isn't susceptible to the IP blocking issues and downtime is. My current web host's support used to be great but is now largely useless.
Backup services would be great, too, if possible.
Do you know anything about Libertyvps.net bitcoin hosting solutions? Reliable or not? Others?

You should pick the top website hosting provider and join in their money making businesses online.

Check out accounts from planethoster.com and inet.ws.
Peerless customer service. Great value! Outstanding tech support.

You, guys, will not go wrong with Libertyvps.net hosting, highly recommend them. Price is reliable.
My site is up, speed is ok, visitors of my site is happy with upload of the pages. Good webmaster tools.

Consider factors such as uptime reliability, customer support, scalability, security features, and pricing when selecting a new hosting provider. The most popular hosting options include Bluehost, SiteGround, HostGator, and A2 Hosting, which are known for their high performance and excellent customer service.

Plans from inet.ws and hostsailor.com are worth trying.
They have a brilliant Support team, always there to help. Super easy to use and fully featured.