Mosquito bites aren't "harmful" as the game has no HP system and you cant die or anything like that.
However, as stated by Alex, it prevents you from catching them. Residents may also have a new dialogue with you. Getting bitten by one also attracts more of them (creating an annoying cycle of stings)
You can avoid mosquitos rather easily, they have a short 'aggro' range and you can hear them coming (high pitched buzzing). They are also very slow moving, so they are easy to catch (once you spot them that is).
In short, they are just annoying. They only appear Summer evenings, though, so be a bit more careful during this timeslot.
Does that mean that I shouldn't give my highest scoring bugs first?
Yes. If you want to get as many items as you can get you should start off weak.
I'm also concerned that if I give lower quality bugs that I'll get lower quality furniture, or will Nat always give you a piece of the Bug set regardless?
How it works is until you meet a certain point level (it was 80 points for me) you will get normal furniture from him every time you break the record. After you break that level of 80? points, each new record after that (including the first) will yield another bug furniture.
So I'm not even entirely sure I can direct the outcome the way I want to but I'd like to try. What should I do to guarantee the most pieces of Bug furniture?
Bugs are graded by three things: rarity (easiest to "manipulate" but you have to find the right bugs), relative length (the game tells you this right when you catch the bug, if you can sort your bugs of the same type by length) and luster/color (this is random and there is no indication of luster until you give it to nat). To maximize the bug items you get, start with not-so-rare bugs and work your way to the rarer ones, working in order of size when you have a bunch of the same bug.
Rarity can roughly be measured by how often you see a bug around. Common butterflies are super common, tiger butterflies are uncommon, emperor butterflies are sort of rare, Raja B butterflies are quite rare, as an example.
Note that the bug off is held monthly, and you probably won't get all bug items in one month. Personally I only managed to get two (I could have gotten more though).
Also not that at the end you'll get a ribbon based on performance. You get a ribbon based on placement, not on how many bugs/furniture you've gotten. A single, high scoring bug will get you a gold ribbon.
Best Answer
There are essentially two upgrades. The store doesn't visibly upgrade at all.
You are given the choice to change your eye color after:
This can be found here.
And you can get the hair styles of the opposite sex after:
Both of the upgrade requirements can be found here as well.