How to check available package version with APT

You can use apt-cache to figure out what version is the first to be installed, ie 'candidate':

apt-cache policy %packagename%

%packagename% stands for package which version we want to check.
Sample output for 'nginx':

server:~# apt-cache policy nginx
nginx:
Installed: (none)
Candidate: 1.1.0-1
Version table:
1.1.0-1 0
500 http://ftp.us.debian.org testing/main Packages

Note: you may want to enable testing repository to have the latest, yet not time-proved versions.

You may also want to simulate install process:

apt-get -s install %packagename%

-s here stands for 'simulate'.