Remote Access from WIndows Vista to a Unix Web Server

Depends on what you mean by "connect to a Unix Web Server". Does the webserver provide its own admin interface over TCP/IP http port 80 or some such? If so just point your browser at the right address/port.

I what I mean is can I use some sort of Remote Desktop application to login to the unix box as if I was at the machine - as I currently do with Windows "Remote Desktop Connection"

I'm not sure yet what the box will have installed on it.  Our hosting vendor is setting that up for us. What are the possibilites and applications that I can use?  I realize this is a very broad toppic  - just looking for general information and suggestions.

Thanks.

To enumerate a couple of ways:

1.  In sure the Unix box the graphical login in (if memory serves its called xdm).  Then install cygwin on your desktop.  In the cygwin prompt run > startx.  Once you get a window ssh over to the UNIX server and then type DISPLAY=<ipaddress of your desktop:0.0>, then type xterm.
2.  You could start VNC on the unix server, start VNC on your desktop giving it the IP address and port of the VNC running on your UNIX server.

There are many many other ways that's just the two I tend to use.

Hope that helps!

Your hosting vendor will probably not allow anything more than ftp, or maybe  a telnet/ssh character terminal connection.  I don't see the need for anything more, if you maintain your website locally, all you have to do is update the changes, and possibly set file permissions.