I have a few friends who live in the UK, who I send mail to.
1st class stamps tend to be used when you want your post to be sent quicker, whereas 2nd tend to be sent later.
If you are send a rather large package, and can't go to the post office, you'll need to put a couple of stamps on the package, as the stamps will pay for the weight of the package. However you can also go to the post office, where you pay around £0.50p - £6.00 depending on the size and weight, and they'll put the correct stamp on for you.
Royal mail is the delivery service in the UK for letters and small parcels. Larger parcels are sent via parcelforce.
The post office is where you go to buy stamps/pay telephone bills/send overseas packages etc.
You can buy and print the exact postage from the Royal mail website - www.royalmail.com/