It might be easier to just ask what you aren't sure of, but a few basics.
- The diet should be simple, all they actually need is water, a pellet only alfalfa based food (like Oxbow Essentials, Science Select, or Mazuri) and hay. Most treats sold in pet stores are not good for them, and a unfortunately many vets just lump chinchillas in with guinea pigs and rabbits and assume they have the same or similar diet. Treats can be given sparingly (a few pieces a week) but should not contain any fruits, vegetables, seeds, nuts, sugars (including honey), or any human junk food. If you are unsure of safe treats just ask and I can give you a list.
- Ideally keep the temp around 68-70F, anything above 75F can cause the chin to overheat and risk dying. That does mean that unless you live in a cool/cold climate year round an AC is required in the summer. Cooling tiles are for additional cooling in an already cool room, like cooling off after running around, and only do any good at all if they actually sit on them which not all chin will even if they are over heating.
- I know you asked about a cage already, but just to be clear chins are not good for free roaming unsupervised. They will 99% of the time chew on anything they have access to eventually. It's very common for them to ignore things for months or even years, giving you a false sense that "they know not to chew on certain things" then decide to chew it up so it's up to you to make sure they only have access to safe things to chew on.
- Wheels are not require and do come with some risks, but if you do go with one make sure it's an actual chin safe wheel. They need to be atleast 15" diameter with a solid metal running surface, there are a few vendors online that make them. The largest wheels sold at pet stores are only 12" which can cause spinal damage over time, and plastic which can cause a blockage and/or gut damage if chewed and swallowed or made of metal bars or mesh that can injure them.
I assume the Yaheetech cage you mean is this one?
It's an ok size for one chin, however not the best cage, if it's what you already have it can be modified to be safe, but if you are still looking I would look for a better cage. Personally I would go with a single Ferret Nation or Critter Nation cage instead, or for a bit cheaper the Prevue Pet Feisty Ferret cage. Both the single unit Nation cages and the Feisty Ferret cage are about the same over all size (slightly bigger) as that Yaheetech cage, and the minimum size recommended by pet owners for 1-2 chins. If you can afford it though I would highly recommending going with a double unit Ferret Nation cage, but if you can't afford it you can also go with a single and save up for an addon later. Both the Nation cages and the Feisty Ferret cage still do need some minor modifications to make safe homes, but I think they are a better design for chinchillas and the nation cages can last decades.
The amount of floor space in that Yaheetech cage isn't great, ideally you want a bit more if for no other reason then it gives you room to put things like the hide out, cooling tiles, litter box if you plan to litter train, tunnels, and stuff like that. You could probably make a platform level for the middle though to help increase the floor area, and also reduce the accidental fall distance. A fall of more then about a foot can seriously hurt or even kill an adult chin if they land wrong (about 6" for a kit under 6 months) so you want everything to overlap, when looking down from the top of the cage you should not beable to see all the way to the floor of the cage if the cage is more then a couple feet tall. Also all the plastic shelves will need to be covered with fleece to prevent chewing, or replaced with wood or metal, easy to do on a ferret nation, but not so easy with the cages that the shelves clip onto the cage. The ramps are not needed so best to just remove and replace them rather then cover them. Chins hop not walk so ledges and perches work much better for them then ramps. The floor is also wire bars, which needs to be covered to prevent foot/leg injury, it's very common for them to get feet or toes caught and broken in wire floors (mesh is "safer" but still not ideal), you can cover with fleece or tile, or both. If the floor is removable just remove it and have them on the pan (again covered in fleece if plastic). The doors are also small which could make setting up the cage, adding things to or taking things out of the cage, and even accessing the chinchilla difficult, which is unfortunately not something that can be fixed. Both the Nation cages the whole front of the cage is two large doors allowing easy access to the whole cage and the Feisty Ferret half the front is doors.
Incase you are wondering, the reason I suggest covering plastic shelves with fleece is that most chins don't chew fleece so you can still use the plastic shelves rather then replaceing them. If they do on the fleece it doesn't shred or unravel into strings like other fabrics so you can remove it before they have had time to swallow enough to cause a problem. A small amount should pass without issue but if they chew and swallow enough it can still cause a gut blockage, so if they do chew it it's no longer considered safe for them and does need to be removed and the plastic shelves replaced with something safe to chew.