I am also new (or, renewed) into the hobby, after many years out of it. I've done a few purchases/trades/sales for the first time a few months ago (though not through here yet, I messed up and didn't track my inventory well, so I'm working on that), and here's my non-comprehensive list of shipping tips:
1) Shipping is (or should be) part of any deal, so treat it as such. The value of what either party receives can quickly go to zero with shoddy shipping. Both parties don't have to ship the exact same way - just that it should be known and stated up front.
2) in general, if I'm sending a higher value card or cards, or if the cards plus protection is more than 1 ounce (max weight for a regular stamp), I'll go for a padded envelope with tracking. If it is a lot of cards, but less than 16 ounces with packaging and cards, I'll use a box and ship that way since it can sometimes be cheaper than a flat rate box. All others I ship in flat rate boxes.
3) when shipping a small number of cards, put the card in a penny sleeve, then in a toploader, then use a small piece of painter's tape (not Scotch tape!) to close the top and keep the card from accidentally falling out. For a larger number of cards, put them in a team bag, with cardboard squares that are slightly bigger than the cards taped to the top and bottom to ship.
4) Since I don't want to end up with a bad name/reputation, I tend to over-protect, even if it makes the package weigh more than the shipping I want to do.
5) Consider buying additional insurance when shipping items over the insurance that is included by the post office. A trade isn't truly "complete" until the package you shipped is in the hands of the other party, and they say all is well. I'd hate to have to refund/lose money or anything like that, especially if it is damaged in transit.
Just my new, two cents
Always looking for Bert Blyleven cards - duplicates are ok!