If you get a dresser/wardrobe/armoire etc., you can interact with it and place up to 60 items (per character) in there. However, even if you have 5 of them, the same storage goes in each one, so you've only got up to 60 items. If you run out, you can either attach items to mail and go to the Town Hall and Save the letter, or create a character merely for storage.
And keep in mind that no living things (bugs or fish) can be placed either in letters or in wardrobes/dressers/armoires etc.
To get more money after your first minor job from Tom Nook, you can...
- Get a Fishing Rod and fish, then sell the fish to Tom Nook.
- Get a Bug-Catching Net and catch bugs with it, then sell the bugs to Tom Nook.
- Talk to the town animals. They may give you a job to do, or give you an item on a whim. From doing the job, you generally get money or an item. You can sell the items you get for money (or keep it if you like it).
- Shake trees. One of three things can come out; money, furniture or bees. Bees are very hard to catch, and will sting you (thus making your face look bad) if you fail to do so. But bags of 100 Bells will come out, and as I said, furniture. You can sell the furniture for money, of course.
