I gather plants by designating the whole map once per season for the first year, but that's really because I want to get seeds of each brewable plant available. I then grow these plants on over ground plots in my enclosed courtyard, where I also have my sheep (for mood wool). I'll consider using DFHack to be more selective to avoid the huge mountains of food that can only be eater (not brewed).
I embark with 3 of each gender of cats, dogs, sheep, turkeys, and peafowl, and slaughter off adults to keep 2 reproductive adults of each gender (got stuck in my current fortress when 3 of the 4 turkeys died at the same turn of year. Managed to capture wild ones to get the production going again).
My main problem is over production of food rather than under production, so I very rarely fish and never hunt (for food, occasional run ins with wildlife happens). Fishing is basically an emergency measure when I get a strange mood requiring shells (has happened twice in total). I do trade for fruit and other brewables since I like to provide as wide a booze variety as possible (more role play than anything else, since it doesn't have any effect unless some dorf happens to be partial to a particular drink). I also grow pig tails and over ground threshables for clothing.
Apart from that, I keep animals that happen to wander into my cage traps protecting the fortress until I reach mastery in training, and then I slaughter them. Exceptions to this are Jabberers and Rutherers which I try to breed because they're cool, as well as GCS' to ensure the ability to run a silk farm.
If I happen to get pairs of giant predators (bears, cats,...) I try to breed domesticated offspring.