I've spent the last few months working on that perfect scoby and am about to start some second fermentation bottles. I've done this several times over the years and my biggest issue is adjusting the taste. By that I mean, it's kind of harsh to me when starting a new scoby and mellows with subsequent batches. While I never have any tummy issues, I think it's better to start out small and gradually increase the amount you drink. When I finally hit that sweet spot with the taste, it's hard to start out slowly.
Edited to add....if you have trouble drinking it as is, mix it half and half with ginger ale at first.