Entry level springer…
Don't slap it open and don't slam it closed. Treat it like it is a finely made machine. You wouldn't do that with a fine skeet gun.
Springers sometimes benefit from a good barrel scrubbing when they arrive from the vendor. You might consider that.
The shot cycle is violent and quite often the screws on the gun will loosen up, especially on a new gun. Taker her down, clean her up real good. Mind you avoid lubes and solvents which could cause detonation if they get into the compression chamber. This is also called dieseling. Tighten up all the screws and put a dab of blue lok-tite on them. Don’t strip them putting them back, just snug them down good and trust the lok-tite to do it’s job. Leave the gun overnight to let the lok-tite set.
Scopes on springers take a beating. If your entry level gun came with a cheap scope, it will probably be ok but monitor the scope’s performance.
Pellets are a big deal when shooting springers. Spring guns are often picky about what pellet they will shoot accurately. If you can afford it, get a pellet sampler and take the time to figure out which pellets in the sampler the gun prefers. That will usually give you an idea as to what pellet weights the gun prefers. Pellet skirts: Crossman Premier is a thick skirted hard lead pellet. They shoot well in a lot of guns. Some pellets that might shoot well in your gun will have soft skirts, prone to damage, examine pellet skirts for damage before shooting
The artillery hold: for now shoot the rifle with the center of gravity sitting on a soft pillow and hold the rifle only as tightly as necessary to maintain a good sight picture. Once you master that, try to accomplish the same thing without the pillow. It will come quickly enough. .
Accuracy in general with springers: There are a lot more people who think their favorite springer will shoot pellet on pellet at 25 yards than there are guns which will do it. Mind you I did not say that there were not any gun/pellet/shooter combinations who can do it. There are enough who can, to make most of us jealous now and then. If your springer/pellet combination will consistently shoot under one mil (3.4 minutes) from a rest, it is doing good enough for the hunting line up. That equates to 7/8″ groups CtC at 25 yards. There are some middle and low power sporters (10 – 14 fpe) that can consistently shoot in the 2.5 moa (5/8″ @ 25 yds) range. There are some light power high quality guns (5 – 10 fpe) that can consistently shoot under 2 moa (1/2″ @ 25 yds) or even a bit better than that. These are not hard fast rules, just guestimations which should help you evaluate how well your shooting with your kit.
Wind: even a little wind can make a big difference with pellets. I read somewhere else that if you scale the ballistics of an air rifle up to compare with a service rifle shooting a thousand yards, it compares fairly closely in range estimation requirements and drop estimation requirements but it is about two and a half times as hard for the air gunner to dope the wind correctly. Soooo….
Welcome friend, you have embarked on a great quest. =)