I had the absolute worst time on the Harvest Festival because I didn't prepare.
http://www.thonky.com/animal-crossing-new-leaf/harvest-festival/
I know you said you didn't want I guide, and neither did I, but I truly regretted not looking at one, once I was trying to gather ingredients. The link is a really good guide on what to expect & what ingredients you need. Especially what ingredients you need! So, Franklin will ask for a combination of fish, fruits, sea creatures & ingredients from villagers for each of his dishes.
I am
terrible at diving, and it was just my luck I was given one of the dishes where he asked for a lobster... I spent 3 hours searching for one, and in the end I had to give up...

I don't TT, so I will have to wait until next year to get the final item...
One thing I would advise is to save after you've completed a dish. That way, if the next dish includes an ingredient you can't find, you can just turn off, and he will give you a different one, once you talk to Franklin again.
The Harvest Festival takes a lot of time & effort, but if you want a good experience, I would gather all the possible ingredients you can before the day.
Also, with your question about the harvest furniture, it is possible to get some from Franklin, but the Nooking's shop was also selling that set all of November... So perhaps look in their shop if you are after some.
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I am so sorry, I mis-read your post about the furniture!! So, the whole point of the harvest festival is to gather ingredients for Franklin, so the town has some food to eat for the festival. There are 4 dishes you will have to make, with 3 normal & 1 special ingredient. If you give Franklin the 3 normal, you will get a piece of harvest furniture. But if you give him the special ingredient as well, you will get a fruit basket, an item you can only receive at this event. You can figure out what the special ingredient is by talking to villagers.
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*3 normal & 1 special ingredient, for each dish.