Equipment and sizing guide
Almost everything on this site needs a mat and space. This page says what kind, what to wear, and what not to buy. It does not recommend brands and it does not sell anything.
The mat
The studies that go to the mat, the sprawl, the penetration step, the double leg finish, the sit-out, the hip heist, the bridge and the referee's position, need a padded wrestling or grappling mat. A carpet over concrete is not a mat and a yoga mat is not thick enough for a knee driven into it. Room mats are usually a few centimetres of closed-cell foam under a vinyl cover, laid in interlocking sections or as a single roll; puzzle-style foam tiles are used at home and are fine for the standing studies and the slow bottom studies, less fine for repeated sprawls. If the only floor available is hard, do the standing studies and leave the rest for the room.
Space matters as much as padding. The motion ladder, the circle study and the lateral step move a wrestler around; two metres in every direction is the least that works, and the international competition circle is nine metres across for a reason.
Shoes
Wrestling shoes are light, high-cut and thin-soled, with a sole that grips a mat without catching on it. They are sized like ordinary athletic shoes in most ranges and are meant to fit close, without the toe room a running shoe has, because the foot needs to feel the mat through them. Try them on with the socks you will wrestle in. Socks alone are fine for the standing studies at home; bare feet are fine on a mat and not on a floor.
Clothing
A singlet is what competitions require and what the model in the viewer wears; a fitted shirt and shorts are what most rooms train in. What matters is that nothing catches a hand or a foot: no pockets, no zips, no loose drawstrings. Headgear protects the ears from the friction that gives wrestlers cauliflower ear and is required in some competitions; it makes no difference to a solo study.
Things that are not needed
No study here needs a partner dummy, a resistance band, a weighted vest or a stability ball. The hip lift shape in particular should not be loaded from this site: it is a shape, and how to load it is a coaching decision. A timer is built in. A mirror or a phone camera helps more than any of the above, because the one thing this site cannot do is look at you.
Sizing the studies to you
Every study is drawn on one body of about 1.70 metres. Stance width, stagger and the depth of a level change are drawn as ranges in the mechanical spec because they vary with the wrestler. Longer legs stand wider; shorter wrestlers change level less far. The numbers on the study pages are the drawing's, not yours; a coach who has seen you move will give you yours.
See also warm-up and cool-down and the training FAQ.