Logic gate symbol vs IC symbol
Please use the logic symbol! The IC is not relevant to the schematic, where it's about the circuit's functionality.  

Most EDA (Electronic Design Automation) software will let you create a component consisting of a package for the PCB layout, and a logic symbol for the schematic capture. For a quad AND gate you'll have either 4 identical AND gates and a symbol for the power connections, or 3 common AND gates and one with power connections.  

When placing AND gates on your schematic you'll start with gate 1 of IC U1. Next gate you place will be gate 2 of U1, and so on. This way you can place each gate anywhere you want, one at the top left and another one of the same IC bottom right if you want. Making physical connections is a problem for later, when you make the PCB layout.  

If your schematic symbol would represent the package you would have to draw all connections for your gates to the same symbol, whether they belong together or not. Your schematic will become illegible. For the PCB that's not a problem; it's not meant to read the schematic from it.