"Index" should do what you want (count starting at "1"). Of course, if you later want to add to your Oystercatcher series you'd be better served using "Counter" and (manually) setting it to start the count at one more than the current number of Oystercatcher pics. Or you could save distinct Presets for Oystercatchers, Robins, etc. The Preset will remember the last variable for "Custom Name" you used. (And if you go that route, you probably do want to use "Counter" and not "Index" -- "Counter" remembers, as you know, the count.)
There is no way to set the options for "Counter" in a Preset other than by editing the Preset. Since the option for "Custom Name" can be set right on the Batch dialog, it seems an excellent idea to have the "Counter" options available there as well. Tell Apple: "Aperture➞Provide Aperture Feedback".
I don't know how to change the default Naming Preset in the Batch dialog -- and I would suggest against doing so, only because it seems to be the kind of thing likely to lead to unwanted troubles with any upgrade to Aperture.
What are you using the numbering of the Versions for?