I always offer 2nd class and 2nd class recorded which is only 68p extra. Out of 800+ items only one has ever gone missing with Royal Mail for me.
Your receipt sounds like Proof of Posting. What you need to do is email the buyer and tell them (as the Royal Mail state) that if the item has not arrived within 14 days you are then able to claim from the post office as the Royal Mail sets 14 days as their target although it should normally be quicker than this.
After 14 days you fill in a form, which you can get from the post office or possibly the Royal Mail website. You send it off, they contact the buyer and if they cannot find the parcel/letter, they will send you a cheque to reimburse you (this can take 3 or 4 weeks and possibly longer near xmas).
If you gave the buyer a choice of postage options, including recorded, then Ebay will be on your side, as they were with my item which was lost. If your buyer paid with PayPal they may be able to claim their money back from your PayPal account without your permission.
Most buyers will be understanding unless you have someone like the guy I had to deal with and will wait for the problem to be sorted out.
My advice is DO NOT refund them as some people on Ebay are not trustworthy, although many are. If you go through all the proper chanels you are doing everything the way Ebay would tell you. Ebay would tell you the same thing, do not refund. You can always email Ebay and ask their advice too