The key is to have a plan and keep cool. The price range of health items is crazy, with VEG being available at 600 at the cheapest, and some stuff like DOM, AYA and SW1 hitting 10,000,000-20,000,000 at the dearest. When you count the zeroes, you see that it can be 10,000 times more expensive to drink SW1 for your health than to eat VEG or drink MEAD. You can be pretty sure that it is not 10,000 times more healthy, though.

So it will probably make sense to have a rough budget and try to aim to finish the quota and by so doing, getting the challenge to the desired outcome. I have seen people including myself ending an easy challenge with half the quota left. That means that you have spent 10 times more money to stuff that is only 2x the benefit.

Of course I would have a lot advice to tell since I designed it all, but it's the joy of exploration that I don't want you to lose. Listening to the other councillors' advice is good as well, since even though they don't know the health challenge, they can read my mind and are quite good in the detective work.

ADD: Okay 2 more helps:

1. The harvest season is starting soon and the peasants are competing to sell their produce here as historically this has been a high-priced market. In 2 days, it is possible that VEG price hits 1,000. Unless there is a bad harvest, which even I don't know (moneromooo knows but does not tell). This, combined with the regulated price of MEAD and BEER is the way to go if you're seeking to combat the challenge having small budget.

2. The frequencyBonus gives you more benefit if you spread out the consumption over a longer time. Maximum benefit is about 300 health points (3% of the maximum Health of a character).