What do I need to look for on a new embroidery machine if I want to do applique as well on the machine?

You can do applique on any embroidery machine but not free hand like you would on a regular sewing machine. Just look for a machine design that says applique and download it into your machine just like you would a fill stitch.
Adorable Applique link at bottom of the page has a free one for you to try.
Hope this helps

All embroidery machines are capable of doing applique. Maybe I misunderstand your question. Applique is a technique.