A host with a good Control Panel will include 'migration' options that can ftp your old site directly to them (with proper credentials of course) saving the time/bandwidth of downloading / uploading everything yourself (and the direct connection is much faster...)
When looking at a new host, also look at space, bandwidth, file (inode) limits.
Many 'unlimited storage' hosts limit the total number of files - which limits your gallery size more than a storage limit.
I have used and recommend (personal recommendation) ICDSoft (www.icdsoft.com
I have used them for over 10 years for a variety of sites and more than a few cpg galleries.
I am a 'reseller' for them, and offer a discount to cpg users. ($25 less than their direct price/year and 30 day money back guarantee)
See details at greggallery.gmcdesign.com