The best time to buy wards is whenever you have the extra money, say about 200g or so. Not enough for an immediately impactful item, but enough for a couple of wards and a pink. You use them whenever you expect them to counter jungle you (look for champs that usually counter jungle. OR if they have the poacher's knife). Or you want to do some counter jungling/invading.
If you notice a ward with the newfound raptor smite reward, I'd recommend keeping a ward there because you know they want vision there and they have to go there to get vision. Sneaky thing I just thought of, discover the ward and don't kill it. Wander around there knowing they will come and be ready for them with an ally or something. Maybe your bot lane duo and bait the enemy jungle to them for an extra kill for your adc.
Best wards for their jungle, I'd say the stealth wards generally. However, a well placed vision could work well too.
Try and anticipate when their camps will respawn. They have a 100 second respawn time now so definitely try and place a ward where you will see the camp go down or at least see them walking to and from a camp or two and make a mental note.