I'm a happy Garmin user so I'll give you some suggestions for this brand. (link)
. Hopefully others will chime in for other brands too.
1. Most accurate sensor/antenna in a consumer handheld gps for use in the woods to mark not only points but also follow/record trails
Look for newer models with a high sensitivity receiver. Generally this is indicated by a "H" or "x" in the model name. Saving waypoints and tracklogs is a basic feature on most models.
2. Ability/ease to download points and trails to create maps on the computer
A computer interface to transfer data to/from a computer is also a basic feature on most models.
3. Quality onscreen maps ...
Garmin offers a wide selection of street maps and topographic maps. As well Garmin has a huge user base which has resulted in the production of homemade maps for many areas. See the GPS File Depot (link)
for some examples.
4. Multiple waypoint and trail icons/colors so I can easily distinguish between different wildlife and different types of sign.
These are standard features on most models.
Most Garmin® GPS units are waterproof in accordance with IEC 529 IPX7. IEC 529 is a European system of test specification standards for classifying the degrees of protection provided by the enclosures of electrical equipment. An IPX7 designation means the GPS case can withstand accidental immersion in one meter of water for up to 30 minutes. An IPX8 designation is for continuous underwater use.
I'd recommend looking at the Garmin 60 or 76 Cx models.