Use CellStyle and RowStyle on DataGrid. DataGridCell and DataGridRow both have IsSelected property that can be used in a Trigger to find out if they are selected.
Something like following should do the trick:
<DataGrid.CellStyle>
<Style TargetType="DataGridCell">
<Style.Triggers>
<Trigger Property="IsSelected"
Value="True">
<Setter Property="Background"
Value="White" />
<Setter Property="Foreground"
Value="Black" />
</Trigger>
</Style.Triggers>
</Style>
</DataGrid.CellStyle>
<DataGrid.RowStyle>
<Style TargetType="DataGridRow">
<Style.Triggers>
<Trigger Property="IsSelected"
Value="True">
<Setter Property="BorderBrush"
Value="Blue" />
<Setter Property="BorderThickness"
Value="2" />
</Trigger>
</Style.Triggers>
</Style>
</DataGrid.RowStyle>
Just play around until you get it right.