As for Forest Chopping, I prefer to Chop Grassland Forests over Plains Forests, since working a Plains Forest for 2 Hammers in a pinch is not too bad when you don't have a lot of Mines to work, and Farming a Plains square just makes it the equivalent of an unimproved Grassland Forest. Farming a Grassland square, however, gives a square that lets you grow your City a bit faster than working most other unimproved squares--so I count it as an improved square.
Also, you want to consider that Forests can only regrow horizontally or vertically, not diagonally. As such, if a Forest is surrounded by Forests on most sides of it, then it is a good candidate for Chopping. If you don't Chop it (what you might call "culling" the Forests), then Forest regrowth in the area sits at a stagnant level (i.e. little to no Forest regrowth is possible). For example, the Grassland Forest 1NW of our capital is surrounded by 3 Forests. It could be a good candidate to Chop, since right now, it cannot help a new Forest to grow, while it is also "blocking" the neighbouring Forests from causing growth/regrowth. However, if we Chopped that Grassland Forest (locatied 1NW of the capital), then we would actually ADD three chances per turn for a Forest to grow. When a Forest grows, it means getting free Hammers from a future Forest Chopping activity.
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Forest Management and Maximizing Forest Regrowth by reading the linked message and the message that follows it.
A further consideration with the Forest Chopping and regrowth management is that if there IS a Strategic Resource (Copper, Horse, Iron, etc) 2N of our capital, then a Forest cannot grow onto that square. In that case, it might actually be better to Chop the Forests that are 1N of the capital and NW + N of the capital, but leave the Grassland Forest that is 1NW of the capital exactly where it is (i.e. don't Chop the 1NW Forest) so as to get 4 additional Forest regrowth chances while getting the Hammers from Chopping 2 Forests.
All of that said, Mosher's idea of sending the Worker towards the south to Chop a Forest there is a decent idea, since we don't need to keep ALL of the Plains Forest squares and moving there would put our Worker close to the Sheep, which is a great idea. Also, Mining the Plains Hills square after Pasturing the Sheep is a great idea, too.
After Mining the Plains Hills Forest, I'd probably say move 1N and Mine the Grassland Hills Forest, followed by moving 1NE and Chopping the Grassland Forest that is NW + N of the capital, then moving 1SE and Chopping the Grassland Forest that is 1N of the capital.
But, lots of valid possibilities for Worker movements exist and if Barb units show up, you often need to change your plans anyway.