Wireless and truly wireless: These connect to your devices using Bluetooth, so you’re never physically tethered to your smartphone, tablet, or computer. Wireless headphones don’t use a wire to connect to an audio source, but they do use a wire to connect the two earpieces together. In contrast, “truly” wireless headphones come as two separate earpieces that don’t need wires to connect to anything. Wireless headphones are incredibly affordable; truly wireless headphones can cost anywhere from $100 to $400.
Circumaural headphones (sometimes called full size headphones or over-ear headphones) have circular or ellipsoid earpads that encompass the ears. Because these headphones completely surround the ear, circumaural headphones can be designed to fully seal against the head to attenuate external noise. Because of their size, circumaural headphones can be heavy and there are some sets that weigh over 500 grams (1 lb). Ergonomic headband and earpad design is required to reduce discomfort resulting from weight. These are commonly used by drummers in recording.
That amp, if in good working condition, has 100 times the potential sound quality that those 2 headphones can play. You could improve the sound somewhat with a careful EQ, since the Marantz will have power reserve to spare. But I’d try to find a better headphone, and there are some bargains out there. If I were suggesting an ortho, I’d say get the lower price Mad Dog, which will give you great audiophile sound with the Marantz.

Over-ear and on-ear headphones effectively block out outside sounds, allowing you to hear your music or whatever else you're listening to crisply and without distraction. Over-ear headphones are sometimes known as full-size headphones because they completely envelop the wearer's ear. This results in what's known as passive noise reduction, which makes these some of the most-preferred headphones available. The only drawback is that your ears and the skin around your ears can get warm and sweaty. These are usually the heaviest type of headphones.