I wrap my 45's with sleeve in newspaper, and then sandwich between two pieces of cardboard, and then wrap that in newspaper also. Insert in a padded mailer, seal shut, add FRAGILE stickers, and it's ready. I always suggest wrapping the record and sleeve with newspaper before putting it between cardboard. I've received records in the past where the record and sleeve were put in cardboard and taped shut, but the tape also stuck to the record sleeve, and in this case, it was a picture sleeve and it was very hard to get the tape off the sleeve without messing it up. So wrapping first before the cardboard is a must.
As for Lps, I usually get 12" x 14" shipping boxes, leave them flat, and then insert the album with cover. With the box staying flat, it makes a tight fit and is very protective. Then just fold and tape the ends over as needed to make a sturdy flat package containing the LP.
For 78's, I go out and buy large boxes, lots of bubble wrap and styrofoam peanuts. Wrap the record like crazy until it's a big bubble wrap ball, and then place in cardboard box with lots of peanuts underneath, to the sides, and on top. Add extra cardboard inserts inside as needed to make a very sturdy box, while still allowing the record to "float" as much as possible. Just be sure to let the buyer know that shipping costs for 78's are more expensive due to the extra materials needed and the weight of the final packaged product.
There is a supplier in the US called Bags Unlimited that sells mailers for LPs, 45's and 78's, as well as CDs, tapes, comics, etc. Their stuff is very sturdy, and I love the unique boxes they have for 78's that include foam pads, but the prices are a bit steep for me, so I don't buy there often, except to get white paper sleeves for the 45's. Their url is
www.bagsunlimted.com if anyone's interested.