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I'm curious about some general guidelines, that may represent a probability although not necessarily certainty, especially when combined with other factors, about choosing the best source of emergency drinking water from multiple available in the general area.

For example, if I'm stranded or lost, would it be a safer bet for potability to look for very small streams draining vegitated hillsides or from a nearby larger stream to which it drains?

In general, you should have some sort of portable water purification system. There are quite a few on the market that are small and portable which should be included in your survival kit. Here is a link for various options available via REI just as an example. Barring these, getting the water to a rolling boil for a minute will work.

I would go for the small stream, particularly a fast moving one. If you can find the spring that the stream starts from can be good or where it is going over rocks. My understanding is that the risk of getting sick from this water is lower (but should be done with caution).

You should also be aware of other methods of collecting water that would be safe to drink. You can collect dew and condensation with a tarp or plastic.

https://inhabitat.com/harvest-water-from-the-air-with-fog-dew-collectors/

Or manually collecting it off of leaves should also be fine.

Melting snow and ice is another option.

https://www.dryadbushcraft.co.uk/bushcraft-how-to/obtaining-water-from-snow-and-ice

In general: the smaller and steeper the stream the better. The two main things you don't want to have upstream from your drinking spot are still water, which is a breeding ground for insects and insect borne diseases, and feces, which can be dropped anywhere but is less likely to be present the smaller the creek is.

If you can follow a stream to its source coming out of a mountainside you're golden, this water was filtered by the soil and is usually very clean. But you have to try and be realistic in looking for it. Going uphill costs a lot of energy. And when you're lost and looking for civilization in particular you often want to be heading down to the valley.

Rain water is also very clean, clouds are relatively bacterium free. The problem with rain is collecting it. Even in the wettest of torrents leaving a glass out for a day nets you just one glass of water. Normal rainfall is more like a few millimeters to a few centimeters. You'll have to use tarps and such to collect rainfall from as large an area as possible.

Snow and even glacier ice are often relatively unsoiled as well, being rain water that has been sitting on the ground surrounded by itself. But you want to melt and drink it rather than eating it, that will cost you too much body heat. In very cold conditions melting can be tricky, requiring fire or alternatively a shelter being warmed by body heat and lots of patience.

In some places you can dig for water, most notably the deepest parts of dry riverbeds and the lowest points of dune landscapes near the sea. (Not on the beach, the ground water is salt there.) How clean it is depends on local conditions. While this water has been somewhat filtered by the soil it also sits relatively still in a place where gravity slowly collects pollution and such. The more deserted the landscape the better.

And then there is the possibility to go for a dirty water source, or even green leaves, and making drinking water using a solar still. Describing how to make one is a bit out of scope for this answer, but it's relatively easy provided you have some form of a clear plastic sheet available and the sun shines. The amount of water it brings you is pretty small though, and especially when you're on the move a readily drinkable source is preferable. There's also the option to build a filter by taking something like a bucket, making a small hole in the bottom and filling it with layers of sand, rocks and if you have it charcoal (from your campfire). It's not as good as the dozens of meters of clean soil on top of a natural spring, and it's not as clean as a solar still, but it's something, and it's relatively fast.