This has been asked before, please do check the forum before posting. However, I do try to be nice and otherwise helpful, so here goes.
According to the official roadmap, anyone who owns a FFXIV service account will be invited by phase 3 at some point or another. There is a possibility that this could change, but with beta most likely starting on Friday, it's unlikely that they will change this. I would expect to see your invite around Tuesday or Wednesday, but keep in mind that they may stagger invites to alleviate server stress. In such a case, you may have to wait a week or two, but there's no information that suggests that they'll be doing this.
Please keep in mind that at least 2/3 of the content in phase 3 was not present in alpha, or either of the previous two beta phases. As such, keep an open mind about testing, and submit feedback accordingly.
This is my sig; Enjoy.
FFXIV: Tom Carroll - Excalibur
FC: Sitzkireg (www.sitzkrieg.guildwork.com)