Hi fent, buy some proper mailers from covers 33 for a start (they come as a minimum of 25, so perhaps you'll sell some more). Mailers look professional and save an awful lot of trouble. Then scrounge some decent heavy weight corrugated card from where ever you can (shops, neighbours etc). You need at least two stiffeners. If the finished package doesn't flex you are probably okay. Finished packages normally weigh around 450-550 grams. That means Royal Mail will be charging around £2.25 inland depending on weight and to add about 60p for packing. USA will be quite a lot more, around £7.00 + packing using RMs small packet service.
I've sold hundreds of lps worldwide successfully.
Any questions pm me.