YOUR ESTIMATE:
The following are rule of thumb estimates for various size households based on
no long walks and a few miles drive to the new place:
A typical one bedroom apartment (600 sq feet) generally has 18 items of furniture and 30 other things including boxes and takes 3-4  hours to move
with two men for an approximate price of            $400-$500
A typical two bedroom apartment (800 sq feet)generally has 24 items of furniture and 50 other things including boxes and takes 4-5 hours to move
with two/three men for an approximate price of   $600-$700
A typical three bedroom house (1200 sq feet) generally has 35 items of furniture and 75 other things including boxes and takes 6-8 hours to move
with three men  for an approximate price of       $1000-$1300
A typical four bedroom house (2000 sq feet) generally has 50 items of furniture and 100 other things including boxes and takes 8-10 hours to move
with four men for an approximate price of         $1500-$2000
The way to figure out if your place fits in to the above categories is to count the number of items of furniture. 
Count dining room chairs, coffee tables, end tables, and anything larger. Do not count boxes, bags,
suitcases, TV sets, microwave ovens, lamps, pictures, etc. These all count as boxes. 
Generally add one hour for each 60-80 walking steps.