Figure on about $30 or so if you pack it yourself. If you take it somewhere to get it packed and shipped, it WILL get expensive.
Careful Packing
You need to find or buy a box that allows AT LEAST 2" of extra room for the front, rear, and bottom of the unit. The top and both sides only require 1" of foam. Of course, more is always better - it all depends on the size of the box chosen. The box can have a single wall, but should have a burst test strength of 200lbs, or you can use any double walled box - if you can find it. A common size that works well is 20x16x4 or 20x18x8 for heavier or Commercial units. Head down to Lowe's or Home Depot and they should have some boxes. While there, pickup a 4' x 8' sheet of exterior sheathing - it's white styrofoam, 1" thick, and has a thin aluminum film on one side and white plastic with writing on the other, the cost is about $30 or so for one sheet and it's light as a feather. This is the stuff you see on outsides of homes when being built - it’s called exterior sheathing. There are other types and colors of sheathing, but they are too stiff and will not absorb impacts like the sheet I’m describing - only use the sheeting that has WHITE styrofoam.
You can cut the sheet to fit it in your back seat - AFTER you buy it, that is. Best knife to use is the Stanley Xtreme Snap-off Knife, which you can buy there as well for $15. I always use mine with the blade fully extended. It works the best to cut this stuff, period. You’ll need to line the bottom of the box with two inches of this styrofoam. BE SURE TO CUT HOLES FOR THE FEET because if the box is shoulder dropped by UPS (it's what they do...) the feet will be shoved up so far inside your unit that it will be damaged - permanently. Ask me how I know?? So, either cut holes for the feet, or just remove the feet altogether. I do not need them, keep them at home. I have plenty of feet that I use here for this very purpose. You only need 1 inch of styrofoam for the sides and top of the box. It will take some time to make the box and no doubt you’ll make a few mistakes. It’s well worth the time, trust me. Be sure that the unit will NOT move around inside the box, when shaken! Also, be sure to tape the box closed in a H pattern, both sides- cover all the seams and make sure to tape the BOTTOM of the box as well. Best to use three strips of tape to close the seam on the top and the bottom of the box. Now, if the bottom of the box is already taped - TAPE IT AGAIN – with three strips. All the insurance in the world will not replace this unit. Best to pack it well!
Shipping:
As for choice of shipping carrier, it’s always best to use UPS. The mail (USPS) is getting more and more expensive, not to mention THE slowest service these days. If you do use USPS, do not fall for their ‘extras’ – tracking, special handling, etc. If you wish to purchase insurance, it would be best to use UPS, as regular UPS Ground comes with $100 of insurance, at no extra cost.
I recommend ShipStation. You'll have to sign up, but they do not require a credit/ debit card. It's free for 30 days, so just cancel after you ship your package – or if you ship a bit each month, keep it for $10 a month. Heck, you'll save that amount each time you ship! - I kid you not. Once you create and then print the shipping label, just tape it to the outside of the box. You can then drop the box off at any Pack-n-Ship place or any CVS or even UPS Drop Off locations. They cannot charge you extra just because you used your own pre-paid label. Ask for the manager or blow them a raspberry and go somewhere's else.
I don't make anything from this referral - I'm just trying save you some hard earned cash.