Make sure you have a large supply of the boxes in all sizes. Order from USPS now if you use Priority Mail boxes. They can take 10 days to arrive during the holiday season, so stock up now!
If you ship clothing or soft goods, consider using a poly mailer instead of a box. They are easy to store and come in a variety of sizes. Here's what a poly mailer looks like if you're not sure what I mean:
I buy my bags and poly mailers from The Paper Mart but you can find a lot of shipping supply sellers on eBay too. Another popular place to get everything from tape to boxes is Uline.
Stock up on tape and bubble wrap or whatever padding materials you need. I keep a large supply of packing peanuts, bubble wrap and blank newsprint so I have some options depending on what I am shipping. I always make sure my item isn't banging around inside the box; it shows that you care about your buyer's item IMO.
I love the Scotch 3M packing tape, it's thick and I rarely have to "pick" at it to get it started if it ends up back on the roll. BJ's Wholesale Club has a coupon right now for $5 off an 8 pack on 3M tape if you have or know someone that has a BJ's membership. Last month Costco Wholesale Warehouse ran a similar deal and hopefully they will run it again before the holidays. Whatever tape you use, buy a large supply so you don't have to fight crowds during the busy shopping season.
I place a high percentage of my items in some sort of plastic bag for protection in case the box gets wet. I have a lot of different sizes of zip-top bags and cello bags. I use these for everything from toys to shoes and believe me it's worth the money. If a mail carrier leaves something out in a huge water puddle doesn't mean the buyer isn't going to come screaming at you because the item is ruined. It may not be your fault but it becomes your problem!
Finally, consider getting some of your personal holiday shopping, planning and chores done early so you can enjoy the season. I try to write my Christmas cards and buy gift in advance so I'm ready and not stressing about everything I need to do to ensure a great Christmas for my family.