As a busy person like everyone else, I’m honestly more inclined to pay more attention to mentions and retweets. Offering thanks with a return mention or retweet is the polite way to give back to your follower, whether new or not.
Direct Messages seem to be a way to self promote tactlessly.
In my opinion, when I follow someone and receive an auto-generated message thanking me (and offering other ways to connect), I feel it is truly thankless. Thank me by following me back or by connecting with me by a retweet or mention. The most infuriating DMs I get are those that are auto-generated to self promote, and you can’t even respond because-ha ha-they aren’t following me back!
It was spoken perfectly in a tweet by @Scarberryfields “My getting one of my tweets favorited is like getting roses. RTs & MEs are great! 1 out of my archives-Priceless!xx”
If you truly want to thank someone for following them, send something that everyone will see (like a retweet or mention), not a direct message that only the receiver will see, with a self promoting message attached. Don’t get me wrong, simply sending a ‘thank you’ direct message is fine. But if you’re like me, you won’t read it.
Use DMs for what they are intended for: personal one-one messages, like sharing an email address so you can communicate further or other personal information that you don’t want the whole world to see, or that you don’t think the whole world will be interested in.
Chances are you’re wasting your time sending DMs, and either you’re insulting the receiver or being ignored. I personally have NEVER used DMs unless it was for something personal, and the message was directed to me first (and the sender alerted me on Twitter that I would be receiving it).
I hope this helps! Happy writing and promoting!