I wouldn't chop everything, there's resources that interact with other game mechanics that you might want to keep, so you need to think about what you might miss later. You want Camps and Pastures as the Cree, for example.
Woods specifically, you should only keep if your city have no other sources of productions and even then only woods that are on a river tile, which give it +1 production. Keeping a wood that isn't on a river is only for completely desperate situations, like no hills at all, no river,no nothing. They are a really bad source of production for most of the game, they get +1 production only in the atomic era!! You don't need it, you don't want it.
Another situation you might want to keep woods is if you care for appeal but that's a really specific scenario. Do you plan to build a national park? Decide where early, if there's woods there don't chop it, it will get +1 appeal later because it's an old-growth wood. This +1 appeal is only applied to the tile where the wood is, not around it like the inherent +1 appeal woods have, so it's only useful for national parks (I learned this the hard way. RIP my Chemamull spam strategy, I kept all that forest around for nothing). Unless you want appeal in early game, you can plant woods in late game, so no reason to keep it around if you only need appeal for Sea Resorts or Neighborhoods. If you gonna keep woods for appeal in early game, if possible keep a wood that is on a river, at least it will be a decent tile.
