WildAtHeart,
Being a textile person I give you a textiles answere. I hope an experienced slinger will give you a slingers answere. I just slung my first today.
http://www.slinging.org/forum2/yabb/YaBB.cgi?board=1;action=display;num=11088454...

I would go for the 2 mm string for the braiding, and go on with the same string for the warp of the pocket. If you start dividing your string in four sections for a few wefts and then divide in 8 and then in 16  you will get a smooth transfer from braid to weave, and do the same at the other end of the pouch to start the other braid. Or start with weaving, ending in a narrow strip at both ends and braid from there.

I would choose the stronger string for the warp, it getting the most wear, (I think) and use the weaker string for the weft. Thicker string is not always stronger, so do a little test when in doubt.

When you say that the thicker string will go faster weaving you are right but not by much. If you use smooth hemp, you may want to get the weft close together but if the hemp is untreated and a little rough in finish, you may leave spaces between the wefts.
Weaving a pouch, even a big one, does not take all that much work and you get more pleasure out of one you think is poperly made.

If you surf the web to a weaving site, look for a warp faced weave, a weft face weave and a linnen weave. (The last may have a different name but I mean the one where all the strands can be seen, like in a bedsheet.)
This may help you find the structure you need.

Succes,
Willeke

Okay, that is sort of what I had in mind as well.

How do you go about weaving? Do you just hold the whole project in your hand, weave another line, and work it back with your hand? Or do you use a loom or something?

I use a 2x4, about three feet long, with 1/2" wooden dowels set near each end, as vertical posts.  I slip the finger loop over one, stretch out the work, and tie it off at the other.  This doesn't provide as much tension as a bow loom but can be easier to make/procure if bow materials aren't available.

ASCII drawing, side-view:

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# = 2x4, | = dowels

WildAtHeart,
While tension on the warp is not absolutely nescesary, it makes weaving so much easier that a beginner would be stupid not to do it.
How to beat the weft in its place depends on the scale of the work more than anything else. For the small size a sling is going to be, a single spike will be enough. I weave small sizes with a heavy needle, (about 2 mm across 15 cm long) or use a nylon netting needle, and use that to beat the string into place too. You can also just use your fingers, I would, but I found that many people find the small controle tiring.
For bigger sizes combs and beaters are used but that is like using a canon to fire a marble.

If you are not sure about what will work, just start and see how it goes. It is easier than it seems. (Little girls are made to do it age 4, and are able too.)

Willeke