This link has some pretty good information on 'Perfect Fruits'. It looks like when you plant a 'Perfect fruit' tree you get a random amount of shakes before it dies. It would be pointless to NOT plant/shake the tree when you have them available. You should always have some perfect fruits on hand for when your 'Perfect Fruit' trees die.
Sidenote from the site: Perfect fruits sold in towns that the fruit is not native nets you 3000 bells (compared to the 600 in your town). So definitely sell your perfect fruits in your friends towns!
Note that you cannot plant perfect fruits of non-native species; if your fruit is orange, you cannot plant perfect peaches; they will instead turn into normal peach trees. However, if you imported a perfect orange into your town where oranges are native, you could plant that orange and it would become a perfect orange tree.
After going through Reggie's house, documenting all the items that he owned that I also had in my catalog, comparing the prices and doing the math, I've found out that ordering an item through the Happy Home Showcase is 1.2x more expensive.
Here are a few of the items for comparison:
Item Catalog Price HHS Price
Modern Wood Stool 1,480 1,776
Dartboard 1,520 1,824
Exotic Screen 2,250 2,700
In addition, you can only order up to 5 items in a single day. I was able to find additional sources confirming this number here and here, though it's still not stated on Nintendo's official website (which is par for the course for a lot of this game).
So if you want to order something, you'll have to pay 20% more bells, but it may be worth it for those items that you really want and/or haven't been able to find yet. Standard limitations on rare items apply here, so anything you can't order normally through your own Catalog, like the Nintendo set, Gyroids, HHA rewards, etc., you also cannot order through the HHS.
Best Answer
Fruit doesn't actually spoil; what happens is the last time you harvest a Perfect Fruit tree, one of the fruits it drops will be rotten. Perfect fruit trees can be harvested a random(?) amount of times and the last time you shake it the leaves will all fall off and you should get a rotten fruit instead of one of the perfects. Ordinary fruit left on the ground can be left indefinitely without spoiling, best I'm aware.
Turnips, on the other hand, will spoil a few days after purchasing because of the "stalk market" depends on scarcity. Rotten turnips, while more expensive, may be easier to obtain if your only goal is the bugs that collect on rotten items.