I had plastic shelves and a plastic litterbox in my girl's cage for a bit. I think it took about a week before she started to chew on the shelves, though that timeframe will probably vary with each individual chin. Some will probably start chewing it immediately, others might never chew it at all. It just depends on your chin. If you do keep any plastic in there, just be sure you're inspecting it multiple times a day for teeth marks, and be prepared to pull it out at a moment's notice if you do see evidence of chewing. If you have any anti-pill fleece, you can use it to cover any plastic shelving, which seems to stop most chins from seeing them as a viable chew toy. If you don't have any fleece (even an old fleece blanket you could sacrifice), you can order it online, or buy cheap fleece blankets to cut up (just be sure to remove any string it may have around the border).
I don't think tile would be too cold so long as your room doesn't get colder than 60F or so. 70F is actually a little on the warm side for a chin, so it's good that your room is a little cooler. An alternative to tile would be to just cover the floor with several layers of fleece. Until recently, my girl was in a cage with wire floors, and I just used triple-layered fleece liners directly on top of the grating. It worked great! You can either sew a simple pillowcase-style liner that encases the whole floor panel (and use an extra layer or two of fleece inside that), or if you don't sew, you can just cut the fleece to size and then secure it to the cage with metal binder clips. I feel like the fleece would actually be better than tile for a baby/new chin, because you're going to want something absorbent on the floor while you're potty training. If you just have tile before the chin is using a litterbox reliably, then your chin is probably going to end up walking through puddles of pee. Yuck! Better to have something down that can absorb any accidents until you get the litter training sorted out.
As for the height of the shelving for a baby....I'm a little unsure about that. I got my girl as a young adult, so I don't know all the rules for kits. I know that even with adults, you want to make sure you have shelves, perches, hammocks, etc. arranged in such a way that they can't fall more than a few inches from any one spot. I have all the shelving in my girl's cage layered so that if she falls off one spot, there's another shelf or hammock no more than 3-4 inches underneath to catch her. And it's a good thing I did, because I've seen her take a few spills when she zooms around at the speed of light! But she always just slips down to the next shelf, acts a little embarrassed, but is totally fine. I'm sure that rule still applies with kits, but I'm not sure if there's a maximum height you don't want to exceed. I'm sure that someone far more experienced and knowledgeable, like Amethyst, can and will give you a better answer on that.
When is your new baby coming home?