I just wanted to share a DM template that has worked for me as an intro when people follow me. Now that I'm almost at 5K I'm more focused on engaging people on DMs than on comments. This might be similar to what Stef has advised:
Hi (name), pleasure to meet you. Thank you for connecting. Anything in particular about my profile that made you want to connect? How’s your journey on LinkedIn going for you?
You could make it personalized, but I haven't.
So far I've used it with 4 people and funny enough I've received essay-long responses. I've gotten info on what they are struggling with, which helps me identify whether or not they are potential leads.
My aim is to send 5-10 of these per day.
Hope this helps!