If you don't want to send it out of the country (and I assume you are in the US), then GIA is the only practical choice among those you mention: AGTA closed their lab about a year ago, and Gübelin is in Switzerland, although they have a "visiting lab" service that goes to New York regularly, so it may be worth inquiring as to timing, costs and booking.

When you say you want "the most reliable report", and "not sure what else you need" what is your question, really? Are you trying to buy, sell, understand what you have?

I also don't understand your question about submitting single stones - in general that's what gets submitted to labs, although some people may send in a batch of stones, they are all treated as individual unless you go for the (rather expensive) matching service.

Go for GIA, then. The Identification and Origin report is going to be a third (or less - CHF/USD has not gone well for the dollar lately) of the cost of its Gübelin equivalent, and it will provide you with the same basic information to a high level of reliability and credibility. If you enjoy reading through all the gemmological evidence rather than just getting the conclusions, get the analytical report (for twice as much money).

The other option, particularly for rubies, is GRS, but again it does mean shipping.

Ellie - what's your agenda?

You have made six posts constantly recommending GIA - which is not a problem - to threads which are sometimes months old. This smacks of shilling.

Welcome to the club, ellie.  I think most of us posted to at least one old thread when we were newbies.  I hesitate to think of the number I posted to, personally, when I came out of lurkdom at first.  You are in good company, and we all approve of GIA certs - at least when they match the stone in question.