...Are you using cPanel? If so, you might be able to transfer all of your clients onto your new server; however, this might be much more difficult because you are currently on a reseller plan. I'm not sure how easy this will be with any control panel as you are a reseller and do not currently have a server. You might be able to persuade your host to be especially nice and do some sort of backup (many control panels, such as Plesk, offer a backup script) and pick out parts of the backup which were on your reseller account. I can't say I know any way to do it though.
I'd say the easiest thing for you to do is keep your current clients where they are and put new ones on your new server. Make an offer to your existing clients to give them something extra if they will move to the new machine (a free month, extra bandwidth, etc) and you should be able to get a bunch of them to move their own sites voluntarily.