Inherited a pcp rifle.

Welcome...from the sound of it, you have everything you need to get started (unless you need pellets too). Did you get instructions with the compressor? There are many brands out there, and they all require some "care & feeding" of sorts. You should be able to find out how to care for your compressor and rifle here on the site. From what I have learned here, one of the more important things is to make sure that you are putting dry air in your rifle. There could be an in-line filter on either or both sides of the compressor (low pressure air drier and/or high pressure air drier). The forums here should help you figure that out.



Best of luck! This is a great hobby and an excellent way to get trigger time that translates across all shooting disciplines. The accuracy these airguns can get is simply amazing!
 
You should also know the filling pressure max of your gun before you fill as well as the pressure it shoots best at. Unless your gun is regulated there will be a difference. Know also that much of your accuracy depends upon the pellet you choose to shoot. Find the right pellet, for your individual gun, and you are in the nirvana state, with tiny groups, else you are in some other place. ;^)
 
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I don't know if you have a GEN 1 or GEN 2 Stormrider, but here is a link to the manual for the GEN 1 from Pyramyd Air:



https://www.pyramydair.com/airgun-resources/manuals/Anleitung_Stormrider-manual.pdf



You can also get to the GEN 2 manual at the same dealer website. Did that Leupold scope come with the rifle? That scope could be the real gem of the entire gift. They make very sturdy scopes. The compressor you posted pictures of looks like it might be one of the many Chinese imports (such as a Yong Heng). I don't know much about those, but people seem to have pretty good luck with them. Maybe post a better picture of the brand name/model number and someone on the forum that owns the same one can link you to a user manual. The black cylinder on the fill probe is a type of in-line water filter, but I don't see any other desicant filter in the setup. That doesn't mean the system doesn't filter moisture using some other means in the early compression stage(s). I just don't know about the one you posted pictures of. Just remember to be careful working with high pressure air. Ask questions, they are free.



Again, it looks like you got a great introduction into the hobby. You should have a lot of fun shooting and learning the rifle. There are probably a lot of posts here on the Stormrider, and here's a link to a video review of the rifle:



https://youtu.be/J6dWpNvZPLE




 
Two gauges means your gun is regulated so you can fill it all the way up to it's max fill pressure. 

A bunch of info on how to treat your compressor here and a how to fill a tank link at the bottom.

Yong Heng post link;

https://www.airgunnation.com/topic/a-dedicated-yong-heng-subforum/#post-1127767

A how to fill your gun with the Yong Heng link is here;

https://www.youtube.com/watch?v=Vytcl9pE9E4&ab_channel=BigBoreAirguns

Oh, and your water pump goes to the bottom fitting on the compressor the top is the return line.

Always remember to purge the compressor high pressure valve before you try to remove fill valve from the gun or foster fitting from the fill valve.

This should get you started safely and shooting the thing without destroying anything anyway.




 
Awhile back in one off the threads where the guy took a fill whip hose to his face, I suggested a section here on AGN for safety notices, reminders, and basic rules that should be adhered to in this hobby. This post is the perfect example of why we need that section. A guy inherits not just a pcp, but a compressor. 


we all do our best to assist the new folks but there should be a section to refer them to, especially when they say they’ve never owned a pcp in their life. 


not to mention it’ll help a new person from damaging their equipment 
 
Get rid of it, it will ruin your life. Eventually your bank account will,be drained from buying more rifles, scopes and pellets!

Well, maybe not ruin your life, but will drain your bank accounts in that you'll forever be seeking that next level of fun!

Do beware, the Stormrider is a great gun, but you'll probably enjoy it so much, you'll want more and more. I started off with cheap springers and moved up from there. By the way, a good springer is a joy to shoot!

and there's nothing I enjoy more than going to the range, and outshooting the powder burners with my pellet gun, or letting them shoot my guns to show how much fun a "pellet Gun" can be.

PCP's are a great arm of shooting. While you have enough equipment to shoot, I would recommend a spare air bottle. These get expensive, as a small bottle can run $400. That's usually a later aquisition. Shoot the gun, fall in love with this type of shooting and then decide how much you'll spend on it (make sure your accounts can handle the purchases............)