There are lots of opiniions on this subject. I use the cheapest Type F ATF in my 05. I change it every other ride. Easy shifting and I personally have had no problems with 3 different 2 strokes that I have used ATF in. Do a search and you will find dozens of threads on this subject, some with some very good technical data. Don't search just for an 03 YZ 250 tranny oil, just use tranny (transmission) oil in the search.
What every you use, change it often. That said, don't spend $7-8 per quart when you're going to change it 2 days later.
As for the amount, put 1 quart in. It is slightly more than the recommended ml amount but it won't hurt a thing.