Cleaning....
Run a patch till it is clean....a little of your fav. cleaner is fine, hoppies ballistol....whatever....squeeky clean.
Shooting....this will get long.
First
Spring guns take time to break in...does not matter metal or what spring...it takes some time....best way to tell is with a chrony.....and don't even bother with that till you run about 200 shots down it.....in some cases more....valves, springs and all need to get set.
Once you see the vel. start to be calm then you are good to go.
You said you already read about the art. hold.....the thing with springers you have to do it the SAME WAY EVERY TIME. you hands in the same place, the same pressure, the same points on the stock....
SPRINGERS ARE THE SINGLE HARDEST THING TO SHOOT WELL. end of story nothing else needs to be said.....and you can double that on any "magnum" springer.
Having bought at the wallsmart you likely got something that says it shoots 5million FPS.....ok you got a magnum springer....see above. Anything that is saying it is shooting above 1000fps in my book is a magnum.
The pellets you likely bought at wallmart are great......for breaking in your rifles....that is about it.....gamo pellets are not very good, crosman not too bad but your gun may not like them....so what you need to do is go to straight shooters dot com and buy their pellet sampler (after break in) then see what your gun likes.
This is a little like 22 rimfire but worse. I found the pellet one of my gun likes then ordered three tins of the same pellet in different head sizes....oh yes grasshopper, head size in the tins are 4.50 4.51 4.52 5.53.....and it shoots all very well, but one is a true one hole group at 50 yards.....yup one hole.....you have seen those amazing groups on the youstubes videos.....what they don't show is all the work in getting there.....no different then working up loads for a PB (airgunner term for powder burning rifle).....you do different primers, powders, coal, bullets weights shapes, truing cases and primer pockets....flash holes....those F class guys get that amazing group by putting in the work.
Now Gamo.....
You are going to real a great deal about gamo being junk.....IMHO it is the users that need education....I hope that is what I am doing here if you read all this.
Gamo is made in SPAIN.....I am thinking they have one rifle not made in spain and it is made in england....they are a very old air rifle company and do make very good items. They are sold to people that expect to shoulder it like their daddies deer rifle and when it does not shoot well bad mouth the product on every forum on the internets. Then they put time into a "good" air rifle like a RWS 34 or PCP (and PCP is a different duck all together).....it is to airguns as muzzloaders are to cartridge guns....and that is a bit too close to compare.
Bottom line power spring guns are hard to shoot, and even harder to shoot well time and time again. It will be like that scene Bull Durham....when meat makes a perfect pitch and says that was beautiful, what did I do. You will put one pellet right where you want to and think of that line (provided you read all this wordy crap from an old guy)....then the next will go way over there and way over on the other side.....it has to be the gun....most likely not....it is you. You are going to think they are crap....really and it can't be you. Give it time....it is hard work.
Keep us updated, we will help any way we can.....join some air gun forums, personally I hate GTA, they have an agenda really, try airgun nation.
Good luck.