DNS Registrars and DNS redundancy

We currently use Network Solutions as our Domain name registrar.
We are thinking of transferring to another registrar.  Can anyone give me reasons to change or to stay ?  

A few times we have had to make DNS changes when Records change or IP addresses need to change .  We were unable to change the TTL to a lower number which could have made the IP address change faster.  We were to;ld other Registrars may be better.

I think I'm looking for a recommendation from an expert on a good registrar , what features or services they may provide that outshine Network Solutions  .

Also one of our main problems is we would like to be able to have redundancy for our DNS, so if our primary sight is down there could be an automatic failover to a secondary sight for am internally hosted website .  I see there are 3rd party services that can provide this type of service  like https://dnsmadeeasy.com/services/dnsfailover/  I was wondering if any registrars also could provide this service.