How to change the host? (AkiraWeb’s going down)

[Parasso]

Hi,
Does anybody here use AkiraWeb hosting? I and some of my friends experience lately some major problems using it – for example:
- statistics don’t work
- cPanel is unavailable
- can’t upload anything on the server
- emails sent to them bounce..

Fortunately my sites still work but it’s I guess it’s high time to change hosting..

Could you advise me how to change hosting without having my sites down?
Would it work if I just buy new hosting, move my pages and then change DNS settings in my domain admin?

Thanks for help!

p.s. LL owners please don’t black list me if suddenly my current host would stop working at all – soon I’ll have new one - thanks