...i still remember my first time lol and it was great!
Congrats on the new purchase!!
About the scope, no red dots for anything close to what you might be wanting to shoot. On a .22 it's just really how much you want to spend...
I'd suggest a 3-9x or something around there...variable power is nice to have. You get what you pay for though. IMO you have a lot of sub $150 choices and then you start moving into the quaility stuff.
About the trigger, it could be your form or it could be you have had a lot of experience with other firearms before? Your trigger finger must release pressure after each shot for the trigger to reset but i can't comment on the stock 15-22 trigger cuz i switched mine out for a Timney awhile ago. Trigger upgrade is a great idea whether it's just a spring or whole new package.
Stock up on a ton of ammo and enjoy!