Does FedEx require luggage to be boxed?
Effectively yes. FedEx's own guide never words it as an outright refusal, but both of the ship options it walks through pack the bag into a sturdy box with 2-3 inches of cushioning, and its label instruction is a tie-on tag secured to the luggage. FedEx also states plainly that it does not accept liability for damage to any type of luggage during transit, boxed or not.
Does UPS require a suitcase to be boxed?
No. The UPS Store's own guidance says a suitcase can ship as is. A box is still offered, and UPS's fee page lists a package not fully encased in corrugated cardboard among its Additional Handling triggers, so the bare-bag route can carry a surcharge a boxed bag would not.
Will USPS price a suitcase?
Sometimes. In our own test on one route, USPS Ground Advantage priced a 22 x 14 x 9 in carry-on but returned no rate at all for a 30 x 20 x 12 in checked bag, even though USPS's published ceiling of 70 lb and 130 in of combined length and girth covers both boxes on paper. Pull a live quote on your own box rather than assuming either way.
Which carrier is cheapest for a suitcase?
It depends on the size, on this test alone. For the carry-on, UPS Ground Saver and FedEx Ground Economy priced within 50 cents of each other, both under USPS. For the checked bag, UPS Ground was the clear cheapest of the five rates returned. Carrier pricing moves with weight, zone and the week, so treat this as one dated example, not a rule.
Is a suitcase protected if it's damaged in transit?
Ask before assuming so. FedEx states outright that it does not accept liability for luggage damage. The UPS Store's Pack & Ship Guarantee covers items the store packed and shipped itself, using materials bought there. Boxing the bag yourself and adding shipping protection at checkout is the more dependable route either way.