Thanks, I feel better about going Tiller now. I feel less good about investing in a coop, 4 chicks, and a silo of hay to feed them.
You'll need chickens anyway if you're repairing the Community Center (unless you get lucky with the Gypsy, but that's unreliable and can be said of almost anything) and to complete the highest-tier achievements. If you're going with a JojaMart membership, they're a lot less important. Ideally you want at least one brown and one white chicken raised to maturity so you can get large white and brown eggs.
Does food quality matter at all when processing into preserves etc? Should I just sell the gold stars?
This is one of the game's annoyances, in my opinion: With very few exceptions, no, it doesn't. Exceptions include large cow and goat milk, which process into gold-star cheese and goat cheese, and large eggs, which process into gold-star mayonnaise.
It does make some sense, though. Crop quality is a way to improve the value of pure crops sold as-is. If quality carried over into processed goods, they'd be even further ahead of crops.
HOWEVER, I should mention that processed artisan goods being very valuable isn't necessarily "unbalanced." You need to sink a lot of resources into the processing gadgets; once crops are grown, you have to pop them into the gadgets and wait quite a while for the finished product. If this only increased the value of the processed crops by, say, 1.2x or 1.5x, it'd be shit and no one would bother (particularly since gold-starred crops are worth about 50% more than base). Instead artisan processes increase the value by 2-3x, depending on the process.
The same is true of cooked dishes. You can use all gold-starred ingredients and it won't matter.
Finally, making the max amount of cash possible isn't necessarily the be-all, end-all. Chances are you'll have more fun if you make a variety of things.
TL;DR: Quality exists to increase the sale value of fresh crops (and raw fish and forage), not to supercharge artisan goods and food.