Use the following, ssc, instead of ssh.  If you just do "ssc remote.com" then it will list existing screen sessions.  Give it a 3rd argument and it will connect to that screen session, or create it and connect to it.  Either way, if you get disconnected you can just do "up-arrow, enter" in the shell to reconnect.  Zero knowledge of screen required!
Edit: Thanks to @klochner for extending this to handle arbitrary ssh options.  You can now use this just like ssh!
#!/usr/bin/env perl
# Use 'ssc' (this script) instead of 'ssh' to log into a remote machine.
# Without an argument after the hostname it will list available screens.
# Add an argument after the hostname to attach to an existing screen, or
#   specify a new screen.  Eg, ssc remote.com foo
# The numbers in front of the screen tag can usually be ignored.
# ssh option parsing by @klochner
my $optstring = ""; 
while ($val = shift) {
  if    ($val =~ /^-\w$/)  { $optstring .= " ".$val.(shift); }
  elsif ($val =~ /^-\w+$/) { $optstring .= " ".$val;         }
  elsif ($machine)         { $tag        =     $val;         }
  else                     { $machine    =     $val;         }
}
if (!$machine) {
  print "USAGE: ssc [ssh options] remote.com [screen name]\n";
} elsif (!$tag) {
  @screens = split("\n", `ssh $optstring $machine screen -ls`);
  for(@screens) {
    if(/^\s*(\d+)\.(\S+)\s+\(([^\)]*)\)/) {
      ($num, $tag, $status) = ($1, $2, $3);
      if($status =~ /attached/i) { $att{"$num.$tag"} = 1; }
      elsif($status =~ /detached/i) { $att{"$num.$tag"} = 0; }
      else { print "Couldn't parse this: $_\n"; }
      # remember anything weird about the screen, like shared screens
      if($status =~ /^(attached|detached)$/i) { 
        $special{"$num.$tag"} = "";
      } else {
        $special{"$num.$tag"} = "[$status]";
      }
    }
  }
  print "ATTACHED:\n";
  for(sort { ($a=~/\.(\w+)/)[0] cmp ($b=~/\.(\w+)/)[0] } keys(%att)) {
    ($tag) = /\.(\w+)/;
    print "  $tag\t($_)\t$special{$_}\n" if $att{$_};
  }
  print "DETACHED:\n";
  for(sort { ($a=~/\.(\w+)/)[0] cmp ($b=~/\.(\w+)/)[0] } keys(%att)) {
    ($tag) = /\.(\w+)/;
    print "  $tag\t($_)\t$special{$_}\n" unless $att{$_};
  }
} else {
 system("ssh $optstring -t $machine \"screen -S $tag -dr || screen -S $tag\"");
}
Btw, there's a trick to forcing an ssh session to exit and give you back your local terminal prompt when you lose network connectivity:
https://superuser.com/questions/147873/ssh-sessions-in-xterms-freeze-for-many-minutes-whenever-they-disconnect