Courtesy of Virtual Town player Aviatrix
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.