Selling bugs is more profitable than you may think. What you need is a plan to attract more bugs. Start a flower garden; some bugs love those. Check the trees and the areas with long grass (even if you've cut it down). Just about everything has some bug that likes it - even things that lower your Beauty Meter, like weeds. You don't want to leave a lot of weeds, but you can leave one. There are other examples, but it's more fun to discover them yourself. If you've cleared out all the bugs, take a break, close down the game, and come back later. You'll usually have more bugs to catch. Check in at different times of the day, because some bugs like different environments, and always check with Mrs. Mottershead to see if she's got new problems for you to solve.

In the early game, the best way to make money is not to spend it. Just as in real life, don't worry about what other people are doing and especially what they say they are doing. It's often not the same thing. Figure out what is necessary to move ahead and what is just fun, and make priorities. Do you need to fix the bridge? Yes, no argument there. Do you need a furnished house right now? I'd argue that you need one piece of furniture - the game will give you hints as to what types of furniture fulfill that need. It's neat when Mrs. Mottershead gives you a popcorn maker, but you don't need it to start out. Sell it.

When the townspeople ask you to do things for you, you can 1) do what they ask, and it will raise their happiness a little; 2) tell them no outright; and 3) try, but don't fulfill their request, in which case they'll forget all about it by morning. Some of their requests will cost you a lot of money. If you give a peep a gold machete and get a lemon maranta seed in return, you just lost about 975 coins. Bad move!

Finally, it gets easier as you get more experience. Have fun and don't worry too much about coins at this point!

P.S. If you have a buck you can spend, buy the Rabbit's Foot.

To add on to Aviatrix's post about the bugs, I've noticed if you play the game at night, there tend to be bugs lurking around the light posts, and (this may have been just a coincidence) but I found a lightning bug hanging out by one of my peeps Christmas lights on their house

Also, there appears to be a lottery event in the game. I'm not sure how often it occurs, but the ticket is cheap (only 10) and the outcome was 500 for one of my townsfolk! Other than that, just play a lot and acquire multiples of bugs for sure!

I bought cheap clothes and replaced the expensive clothes the townspeople were wearing, and sold the expensive clothes. Trading a collared shirt for a screen printed tee shirt brings a profit of $300+.
On the other hand, if you like the cute outfits in the store, you may as well put them on the townspeople, because they're there forever, unlike the temporary mayor. I do switch my mayor to a cheap nightgown or jammies just before retirement, the one piece for 129 coins is cheaper than a whole outfit.
Also, only buy apple trees, because you can get golden apples. I've had as many as three in one day. There is no advantage to orange and pear trees, and the pears are really hard to see against the grass.

After you build your house your secretary brings a house warming gift. As long as it is the only item in your house (and no upgrades have been made) you can put it in your inventory, go outside, go back in and it will be there again. Do this over and over until your inventory is full then go to the store and sell it all. Do this repeatedly. Tons of $$$ fast and easy.

Is there advantage to having golden apples other than selling them or is that their only purpose?

No advantage. In fact if you don't sell them I think the peeps find them indigestible so there is a positive disadvantage if you don't sell them.

Woah! Really? I have to wear my glasses when I play because I have not noticed golden apples! *rushes off to play*

Later in the game, you can sell the blue roses. I think they're $100 or $150 a piece ~ and they multiply when you plant two together. But by the time you're able to do that, money likely won't be an issue.

There's a 4th tier flower that is generous on sell-back too. I want to say it's either Roseacea Fern or Jalapa Tree. However, Blue Rose Rosebushes are much easier to obtain early in the game. You're right, Zia - I have both Roseacea and Jalapa Tree self-spawning a couple of plants a week, but I also have 600K coins and get over 10K in interest each day.

Guess it's time to build out the house and buy some furniture.