maybe i misunderstood, if you have a 2L, I would use that...
1L will get you by if that's what you got, even without a stir plate. You could also sanitize a 1/2g growler if you've got one around and use it. I don't know that shaking it every now and then will do much for you.
Edit: You of course can't boil it in the growler, so that is the downside of that. You must make it in a separate pot - again, no big deal.
How big of a batch?
Make a small wort, ferment it, pitch it. It'll work out.
...but if you do want to overthink it, there are calculators out there to help you calculate required pitch rate, and there are other calculators that will tell you how many generations you must go given starter vessel volume and starting yeast count to get to a specific yeast count. I think some even designate if there is a stir plate or not.