How quickly do masters students and/or PhD students move from being TAs to RAs? To support myself while studying, I'd find it ideal to be paid doing work or research that advances my credentials. (TAing is definitely educationally valuable for both a TAer and students, but I feel that, unlike RAing, it loses its value after a while).

If it is common for graduate TAs to eventually become RAs, then how quickly (if at all) does this take place for either masters (2-3 years) or PhD students?
The answer to this question is that there is no general answer.  There is so much variation between and even within fields and programs that any definite answer would likely be misleading.

You should not attempt to answer questions about graduate stipends by polling the audience (nor even by phoning a friend!).  These are questions that you should direct specifically to each and every program you are seriously considering.  Don't be shy: you have a right to know these things, and people will be happy to answer you, although the answers may be a bit complicated.

By the way, you write:


  To support myself while studying, I'd find it ideal to be paid doing work or research that advances my credentials. (TAing is definitely educationally valuable for both a TAer and students, but I feel that, unlike RAing, it loses its value after a while).


If you are not yet in a graduate program, you may not know what kind of support you'd find ideal.  I would also suggest you think about (i) how much money you are getting total and (ii) how many hours of work "for someone else" you have to do for that money.  In many cases, graduate students are paid for much more than the work they do for someone else, and thus they are de facto getting paid to do research that advances their credentials (i.e., their thesis work).  TAing for 10 hours week could leave you more time to get paid to do work that advances your credentials than RAing for 20 hours a week.  Or not: it depends on what you are getting paid to do.  Finally, TAing does not necessarily "lose its value after a while": if you are seeking a career at an academic institution which prioritizes teaching over research (note that well over half of all colleges and universities in the US fit in this category), then having a strong teaching portfolio could turn out to be much more valuable than another routine publication.  Or not: again, it very much depends on your situation...