For security over the internet your best answer is Virtual Private network (VPN). Checkpoint has a nice system, and Cisco's seems to be one of the top dogs too. But as always, budget can be an issue. The default "Microsoft VPN" seems to work pretty nicely, for occasional use, but for many users, will be more headache than it is worth! PC anywhere can be an issue for security, it does have some securtiy holes in it, and people are always scanning for open servers.
As far as backup, worry about your server, and if they don't get the files on your server, it is NOT your issue! You cannot manage remote users for backup. You can set policy, and make recommendations, but don't take responsiblility, it will bite you. Tell the users, the best way to keep the data safe, is to have it on the server! On the server, with backup, and there is little chance of loosing more than a days work. keep it on a laptop, with users in charge of backup, and weeks, or months of work can be gone inseconds! I agree with the statement above, for connectivity. Need more info. Broadband solutions ARE recommended! They are more expensive, but people can do their work faster... with "syncronisation" I am assuming you mean files and data. Synchronizing files can be done in many ways. I recommend that the users keep their files on their local machine, and at the end of each session, copy them up to the server.. this can be done with a batch file over VPN, or manually with PC Anywhere, or manually thru email even.
So, to summarize, get a VPN solution for your internet users! RAS is fine, broadband is better. PC anywhere, take it or leave it, but evaluate it. backup your server, and tell the users you can ONLY guarantee that files on the server are safe, and current within 24 hours (or less). I hope this helped! Congratulations, and good luck!