I've suffered from severe Anxiety/Panic Disorder and mild Depression since childhood, and I found in the past several years that having my dog with me has helped me GREATLY in keeping me calm when going into public and even allowing me to go places without another human accompanying me.
Well, my precious Chihuahua, Carlos, passed away last July (he really wasn't PSD material, he could be too protective and aggressive).

I just got a new Chihuahua puppy, Maximus, earlier this week. Prior to seeing the puppy I spent some time with the parent dogs (which I think is important because dogs tend to inherit certain traits from their parents, like people). They were both very personable, sweet, quiet, non-hyper dogs, which was one of the main selling points for me.
(I wanted to go with a Chihuahua because I know the breed well and I need a small dog I can hold to help me feel more calm)

Maximus is 9 weeks old, and I'm just wondering besides potty training, what other basic training is he ready for at this age? And what age should I start implementing other training?
Also, since he is a tiny dog (he will mostly be carried), are there certain things he won't need to be trained in?

I have experience training dogs, I went through some excellent puppy and dog training classes with my previous dog, but he wasn't being trained for PSD and he was a bit older than Maximus.

Any help or tips is MUCH appreciated! Thanks!