The shutter is the part that wears out from actuations, but typical numbers of actuations are normally quite high (50 to 100k+ on a cheap shutter) and replacing a shutter is generally a small fraction of the cost of a new camera. The big thing when buying a used camera is you want to know when it will need a new shutter to know how it should impact the price you pay for it.
As for your usage, you should be fine shooting 3000 in a month. I do wedding photography and will shoot 3000 photos in a day. I do have a higher end camera that fails about 1/3 as often as yours, but at 3000 shots a month, you would still be using it for years before you would need to replace the shutter.
To give you an idea, even on my professional camera, the cost per time I press the shutter release is still primarily the cost of storing the image. The cost of each shutter actuation is measured in small fractions of a penny, so putting a number on it, 3000 photos only really costs you about $7 in shutter costs (rough estimate based on 100,000 shutter count failure and $250 replacement cost). That's less than you would spend buying and developing a single roll of film.