I would count at least the first three of each. After all, you're fairly likely to use those in upgraded form in War; I know I did several times in War 4. Unless you are a general/lieutenant or capture the relics that this war introduces, you won't be using more than 3 upgraded cards, so listing 20 upped water towers is going to be misleading. Generals are just looking for rough guidelines to how many upgrades you have anyway; they aren't going to reject you because you have 49 upgrades and the next guy has 50. They'll care far more about your competence than your card collection, though you'll want at least enough that you'll be able to play any deck they build for you. You should have or be able to buy any unupgraded card, have several of each rare, (don't worry about shards; they're banned in War) and either have enough electrum or time to grind that you can obtain 3 upgrades each week, or have a lot of upgrades already.
Nymphs are nice to have, but not required, especially in elements whose nymphs suck. Last War, for example, I can only recall three teams using nymphs. (time, entropy, and air) Nymphs are normally listed on the auction form as well.