Auth-proxy will authenticate the user only via HTTP, before they can send ANY traffic out. Going by your description this is not what you want.
Lock-and-Key might be more what you want. See here for details:
http://www.cisco.com/univercd/cc/td/doc/product/software/ios122/122cgcr/fsecur_c/ftrafwl/scflock.htm
You could define an ACL to the inside interface allowing everything EXCEPT HTTP/HTTPS. Users doing FTP can just go straight out as normal then. Then define dynamic entries to this ACL that allow all traffic. For anyone to go out with HTTP/HTTPS they'd have to telnet to the router first, put in their login credentials, then they can browse out. Something like the following should work for you:
interface ethernet0
description Inside interface
ip address 10.1.1.1 255.255.255.0
ip access-group 101 in
access-list 101 deny tcp 10.1.1.0 0.0.0.255 any eq 80
access-list 101 deny tcp 10.1.1.0 0.0.0.255 any eq 443
access-list 101 permit ip 10.1.1.0 0.0.0.255 any
access-list 101 dynamic mytestlist timeout 120 permit ip any any
line vty 0 4
login local
autocommand access-enable host timeout 5
It takes a bit of user education in that they will have to be told how to use this (first telnet to the router at 10.1.1.1, login, then you can use HTTP traffic outbound), but should give you what you want.