The first months or so are very important. Just make a good impression there.
My take is the Thank You letter is somewhat meaningless after you are already been hired.
The last job that I got, I didn't even send one out-though I should have and wanted to. I was interviewing at a lot of places, was working and was busy.
I forgot one of the interviewers' names. Also, the interview was mainly them drilling me on questions, so along with the lack of names, I didn't even know what to put in the draft. Thank you for drilling me on questions and exhausting me out.
I felt emphasizing my skills and background was somewhat redundant from my resume.