Get a Garmin GPS unit. ...accuracy of about +- 15 feet to 20 ft. Maybe an eTrex 20 which is about US $200. But look into what models are available. I have an eTrex Vista HCx for bush walking. I get 5m accuracy from it even in very steep gulleys.
When you are at a new tree just add a waypoint. You can just click a button and add a location and even give it a number.
Then download QGIS from
Welcome to the Quantum GIS Project which is an open source (and free) GIS application and you can read in the waypoints and create a map of them and keep you map up-to-date with new trees. Make a layer of "new trees" and maybe a separate layer of "diseased trees" or "trees to cut down" etc.
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The QGIS would work on your main Windows machine. You save the waypoints in the handheld GPS unit then the crappy Garmin software running on Windows downloads it from the GPS unit to your PC. It can save it in an open format called GPX (it's an plain text XML file of points). That can be opened and edited in any plain text editor. The GPX file can then be imported into the QGIS program. You can also if you have an aerial picture of your forest/farm have that as a layer in QGIS. So that's really all done in Windows. Use the Garmin in the field just to get GPS locations and also to navigate you to a specific spot.
Basically I think the Android phone wont cut it for what you want to do but a Garmin + QGIS will. Besides its always fun to play with technology on your farm
Mike