You have the right starting place. Copy tpl_product_info_display.php to your custom template directory, and rearrange parts for starters.

All the elements of the display are marked by <!-- bof something --> and <!-- eof something -->. You can move any of those elements *in its entirety* to another location in the file - just don't put one inside another. So put them in the order you want. Then if the title is next to the image instead of below it, add a line

<br class="clearboth" />

to the end of the main image element. This will force a completely new line.

See the FAQ's for info on making your own custom template, if you don't already have one.