Mooving to a new Server

[Sattva]

Need to move a server to another host with new IP.
Advice needed.

I know how to moove operation system with all drive partitions with R-Drive or Acronis, but here I can't start ISO-images.

Installed Vesta CP in 2013 on a VPS and setup some 10 users and 20 sites and it works fine on CentOS 6.4.

With this VPS provider I don't have access to insert ISO-images and make a clone. I also can't copy Virtual Machine as provider don't let me do it.

Now I have another server and need to move.

Should I install a new CentOS 7, new Vesta CP with new MySQL, PHP, Exim and move all sites manually?

Or there is some tool to make transfer and upgrade less painfull?

Should I edit all DNS manually to change IP for every site and MX records? (this will be some 50 records).

Thanks in advance for help.

[mehargags]

Why not just backup from old server and try to restore into the new server ? I think it should work without fail.