I looked at quite a few before buying one and then buying a house with woodland.
I'd still look at local estate agents for woodland, or farms/land being sold off in lots as, sometimes a few acres of woodland turn up. I wonder with the new IHT laws if some farmers will be forced to sell off unwanted woodland. It can even be worth talking to vendors of land as they may have a bit of woodland that they may sell.
Along with obvious rights such as footpaths you also need to look at any other easements that someone could claim. Does neighbouring land drain into yours, do you drain elsewhere, has someone been given access for years to shoot foxes and could they claim any rights? Are there any services in, over or under the land such as electric, water or telecoms?
Having a good chat with the vendor, local people and having a good solicitor who is used to dealing with land is best.
Other things to consider is access, some woodland may only be accessed over a field which could be waterlogged for half the year. Better private access may mean you have to pay to upkeep the track, road access may lead to fly tipping etc, etc.
It is worth having a good look for invasives, not just the obvious japanese knotweed but there's a long list these days. You may be liable if they spread.
Taking a realistic look at the woodland is useful, having huge trees might sound nice but would you be able to do much with them? Look out for diseases and problems, large ash next to neighbours or a road would be a big liability! A good mix of trees would be ideal in this age of a new tree disease appearing every year or two.
Look for pests, the obvious grey squirrel can do vast amounts of damage and control may not be straight forward these days. Deer, rabbits etc may require expensive fencing. Other wildlife might be lovely but can be a pain - a badger set right next to an access track could stop access for example.
Sporting rights should be on the deeds but a good, experienced, solicitor should advice. I specifically asked mine. Even so you may get the odd chancer like a local fox hunt or shoot.
If you get advice don't take it as gospel, I've had advice from the FC, wildlife trusts etc and found it very much "do as I say not as I do" stuff and can often be contradictory.
I could go on, happy to answer any more specific questions.
Edit to add, also check that the woodland does not have any outstanding obligations or access from historic grants, felling licences etc. You should be about to check on the FC site or via the governments magic maps.