Good for you. You will have so much fun on eBay. Just watch those feedbacks for sellers. They are really telling and will help protect you from bad sellers.
About your transaction. You should get an email from the seller which occurs automatically through eBay. You may get basic 'You've Won' email or if the seller uses the advanced features, you will get a more detailed email. If you don't, be sure to followup with your seller (a day should be plenty of time to wait). If you don't get an email, check the ad, you may not have been the high bidder. Winning bids may have come in 'nano seconds' after your last bid....
If the email doesn't have the address for your payment, you need to email the seller. If they have 1,000's of feedbacks, you may never get a response (they get lots of emails) and you may be forced to use paypal to protect your feedback rating.
The other answers are correct about the seller accepting checks. Sometimes sellers don't accept checks. How they accept payments is listed in the ad. If they do accept checks, you should expect to wait until the check clears your bank before the seller will ship.
I can understand your hesitation about using paypal. But there are advantages to using paypal. Even though there is a small transaction fee to use paypal, it really paid off for me on two occassions they had to go to bat for me to get my money back from a bad seller. Seems to be that in the collectibles area, you might find a lot of 'fakes' so using paypal would be a real bonus.
Ebay has lots of tutorials. You can find the tutorials by going to "Help". Here is a link to the getting started buying on eBay.... http://pages.ebay.com/help/buy/buy_getstarted_ov.html
Remember, eBay will NEVER NEVER NEVER send you an email with questions about your account. Don't respond to those types of emails.
Finally, have fun on eBay. Under the "Buy" button, you will find a small underlined 'Advanced Search' link. Follow that link, enter the search term for the item you are thinking about buying, click the 'Completed Listing Only', and then "Search". You will get a listing of completed sales and you can get an idea of what the item is selling for....
GOOD LUCK and have fun!