Hmm, good question.
If its for home use, I always suggest people start with making hosomaki (small rolls) they’re easy, fast, you can use vegetables as filler if you don’t have access to sashimi grade fish and they’re pretty acceptable in changing flavours to suit peoples tastes.
A makisu (rolling mat)
Short grain Japanese or califorin rice
Nori (the laver)
sushizu (the vinegar)
Wasabi (fresh or tube is leagues better than the powder)
Your choice of fillings
Gari (pickled ginger)
Konbu (kelp) *optional (I cook my rice with a single 2x2” strip inside the cooker to help remover odours the rice may contain.)
Make sure you buy a good quality short grain Japanese rice, hikari or koshihikari are available in most Asian supermarkets. Wash the brine off incredibly well (6-7 washes) and leave it to sit about an hour before you cook it. When cooking the rice, use about a 1:1 rice/water ratio as you want it a bit hard coming out of the cooker (it will soften up when you add the vinegar)
As soon as it comes out of the cooker, transfer to either a soaked wooden hangiri or a flat plastic tub (no metal bowls) and spread the vinegar on top. Softly ease the rice apart with a shamoji and try to separate it into the point where you can see the individual grains. You don’t want clumps (as for quantity of vinegar, I prefer a lot, but to suit your needs its best to do a trial.)
Fan the rice with a hand fan for about a minute, then flip the rice and break it apart again. (Gently, you don’t want to break the grains). Quickly transfer the rice into a room temperature container with a lid, lay a damp towel over top and seal it.
The rice is by far the most important part of sushi, which a lot of people over look, so always try to improve it.
As for rolling, there’s dozens of online tutorials out there, so I’ll save some time and tell you to look them up. But to avoid the bad ones, look for a finished product that has nice, clean edges, centered fillings and evenly cut pieces. And just remember not to squish the rice to the nori and to always use slightly damp and very clean hands when handling the rice.
For cutting your roll, wet the blade of the knife (sharp as you can get it) and cut the roll in half in one drawn motion, don’t squeeze down or chop it. Then put the two halves together and cut them in 3rds.
Garnish as you like.
Remember to always be super clean, and keep practicing. :)