Hi Black.... welcome to the asylum.
I was just wondering if it gets any easier to feed shells into the cylinder (correct me if that's the incorrect terminology), as the spring wears out.
If the magazine spring is even decent quality, you'll be waiting quite awhile for it to "wear out".
New shotguns can be a bit stiff when loading the magazine tube, and may simply require a (very brief) bit of break-in... or in your case, you may simply not be use to it. Do you have a friend that is more familiar with shotguns? Ask them to try it.
There can be numerous reasons for issues not involving break-in. You don't mention the brand or model, so lets start with generic issues... but typically those that apply to inexpensive shotguns.
The fit of follower to magazine tube can be snug or dragging. The tube itself may be rough on the inside or have burrs. The mag tube spring may be stiff, or overly long (14" to 16" is a fairly common value for magazine spring free length past the end of the tube with the cap removed). Going a step further, with issues less common, there may be a dent or bend in the tube that creates binding and friction.
All the things I've mentioned are easily identified, some easily corrected... some, not so much. New gun, issue not immediately and easily correctable
... like exceedingly long a magazine spring for example... take it back to where you bought it, or send it to the manufacturer for repair.
Target loads are "birdshot"... there are several sizes of birdshot, and buckshot as well. The Wikipedia article
actually covers shot shells quite well.