I us FedEx - they tend to be more reliable than others. FedEx always asked how much I want to insure it for. They probably have an upper limit. I;ve never been asked to insure it through a 3rd party.
If the buyer meets my asking prince I'll pick up shipping. If not, we'll negotiate or they will pay. People are now used to free shipping so be sure to stipulate shipping prices and expectations BEFORE generating an invoice.
Always ship in the original box if you have it and if it's in good condition. Manufacturers use them to ship units across the country so they should be okay to use again. However, if the box is compromised at all, find a bigger box to use for double packing. Shipping companies are loathe to admit fault and will find every weakness in your packing. If FedEx packs it themselves, then it's on them.