As Bensch said you batch delete by marking photos as rejected at the end of a session, or you can delete them individually or in a small group by highlighting.Simply highlight the ones you want to delete by clicking command - (control on windows, etc on the first one and then each other one that you want to delete. Then hit the delete key and a box will pop up asking if you want to "delete from disk" "cancel" or "remove".
Delete from disk does just that and if you shoot raw + jpg both those files are off to the trash file. I don't know about the other programs but you've instantly got the database (sorting) you wanted and any adjustments you make to the image are written a sidecar file so the image file stays the same file.
I transfer my files from the sd card using LR with the import - copy command, then check they've transferred ok. Once I've checked that I delete them from the card in camera. This gives me a little breathing space. The last time I formatted straight away was in 2015, something went wrong, no chance of recovering from the sd card. Must get back to Borroloola one day.