There are no good shipping carriers right now. Just do not use USPS. That is my only advice. We have had the best luck with UPS most recently. Although, depending on where the resident is located, sometimes you get a “remote location” fee. Not common, but a watchout.
Cardboard box is fine, just put multiple layers along the bottom and sides. Then use a ton of newspaper or packing paper all around. Some folks use empty water bottles to take up more space if readily available. This is the lightest, most efficient way possible.
As for price, they are all going to be more than you want to pay. If you know someone with a business account, see if they can print you a label. We do this for a lot of our customers shipping to us. Then you can drop it off at a UPS store.
Recently shipped an entire motor package. I needed (2) 16x16x 16 boxes. I specifically went with heavy duty ones and also lined the inside with 1/4” wood than filled it with bubble wrap and other soft cushion material. The entire cost was around $160 from the Midwest to California. I forget the cost breakdown but the box that had the motor weighed around 35lbs. I went with FedEx and used the buyers account cause it was $30-40 cheaper
A number of years ago I parted out a wrecked car, so I’ve shipped everything from auto glass to whole car doors, seats, and frame parts.
As Sam mentioned if you’re shipping a pipe and accessories you’ll want to ship in 2 separate boxes: one for motor/carb and another for the pipe and accessories. You’ll never be able to securely package a box big enough for both without things flopping around and getting damaged.
Derek is correct with using heavy duty packing paper, stuff it in there tight so that nothing can move. Don’t use packing peanuts, they’ll compress with the weight of a motor and loosen up. Things get damaged in shipping when items are able to move around inside the box! If you can shake the box hard and anything moves inside it won’t survive ground shipping.
Double boxes for the motor is a very good idea. Something like 14”x14”x14” inside of a 16”x16”x16” with more paper in-between. For the pipe and lighter items a single box packed well usually works.
When it comes to shipper cost size is typically a bigger factor in cost than weight. Make the package as small as possible to reduce cost, but don’t skimp on protecting that motor. You can also cut down most boxes to reduce their size if needed for thing like the pipe.
I’ve found that FedEx is easier for me to add the $3k of insurance to when shipping my KA, but it could also just be my local UPS that sucks as the stores are franchises. Use their online calculators to get a rough idea of prices. As Derek said don’t use USPS for something important like a motor.