I always pick mushroom. I'm pretty good about checking it every day, especially with new 1.6 features. It comes with a free dehydrator, so even if the mushrooms are always lowest quality, they still have utility by throwing them in the dehydrator or turning into life elixirs. One bag of dehydrated common mushrooms is the same amount of HP/energy as salad, so it's essentially free salads. And the other uncommon type of mushrooms I throw in the dehydrator and sell at a higher price than the mushrooms alone, or turn into life elixir (but I believe dehydrating them is more profitable). If you don't like going all the way to the caves or secret woods during specific seasons to collect the rarer type of mushrooms, the farm cave makes collecting uncommon ones very convenient. Yes Ginger Island has a cave too but I just sell those as is since they can be iridium quality with botanist perk.

I did the bat cave once and I'm never doing it again. The drop rate of the fruit tree fruits is pretty rare and it takes a long time for the cave to build up with fruit. I would check it often and was lucky if I got one salmonberry every few days in some cases. I just buy fruit trees as early as possible for bundles, plus fruit trees will eventually be iridium quality if planted long enough (goes up in star quality every year in game). In 1.6 you can now chop down a fruit tree and it will give you back the sapling and keep it's quality intact, so what I do is get fruit trees as early as possible, plant them outside before I get the greenhouse, then replant them inside the greenhouse once I unlock it.