You should be able to look in (with a flashlight) and see where the bearings previously rolled. There should be a pencil thin track. If not, I'm still pretty sure its the outer "race". You don't need to account for where freehub ends and hub "starts," because the race on drive side is actually built into the freehub, not the hub body. If you change out the freehub, you get a new drive side race!
Here's a page w/ diagrams that helps explain where bearing placement is on freewheel vs. shimano cassette hubs:
http://www.sheldonbrown.com/brandt/free-k7.html. Seriously, I'm pretty sure you want the outer race, not inner. Think about this, when you tighten in the cone, how will it reach the inner race?!?? And even if it did, the flats would be hidden in the hub and you wouldn't be able to tighten against locknut! If in doubt, call or drop by local shop.
ALSO, in 98% of wheels you want 9 ball bearing on each side of rear hub, 10 in a front hub. You might be missing two. When packed, it should seem like you have just enough space for one more bearing in the race, but if you actually put it in (in most cases a 10th bearing), all the others get displaced.