So, I'm not exactly sure what the "over the shoulder" thing means.
Chins need to feel supported when picked up like a guinea pig. However, chins have a "floating" ribcage that is very easily injured. So you never, ever want to squeeze a chinchilla across the middle.
The main thing is to give your new chin time to get used to you. Do not chase him/her around trying to catch them, do not force them into your lap like you might a guinea pig. With chins, everything is to be on their terms for them to best and most comfortably get used to you. Chasing your chinchilla around in circles and trying to "grab" them out of the cage is a common mistake early on. Chins have extremely long memories! I would spend time sitting next to the cage at first. Talk to him, sing to him...
Chins will also chew anything and everything. You cannot have any plastic in the cage. Even a small amount can result in a GI blockage. In my opinion GI problems are even more urgent in chins than guinea pigs.
While many guinea pigs do not "enjoy" being held, the majority of chinchillas will spend most of their life barely tolerating it. They will squirm and such. Some do like light rubbing (called scritches) behind the ears or on the chin, but not all.
Males need to have a hair ring check. This is where you check the hair around their penis as it can get clumped up around there and cause them extreme discomfort.
Chins need a simple diet of a high quality pellet (Oxbow, Tradition, Mazuri), fresh timothy hay (APD, Kleenmama, same hay this forum considered good for piggies), and water. They are sensitive to giardia, so tap water and brita type filters are not okay. I use reserve osmosis filtered water available in big jugs from the grocery store. You can also bring your own bottles and use one of those filling stations. Just ensure it is reverse osmosis filtered.
Chins should not be fed vegetables or sweet treats. As with guinea pigs, most of the things in pet stores are bad. They cannot process sugar in their system. Raisins, the once popular chin treat, are now frowned upon. Good treats are the occasional unsweetened shreddies cereal, non instant oats,
Chins teeth grow fast and are not generally kept properly short from pellets and hay like guinea pigs. They should have things like natural pumice, loofah, untreated apple sticks to gnaw on.
C&C cages are not good for chins and you can read about that in other threads. Ferret Nation cages (with plastic removed and untreated pine shelves in place, home-made melamine & wire, quality cage, and Martin's all make good chin cages (google is your friend, I am not).
Store-bought wheels are dangerous. Quality cage sells an excellent wheel as well, the Chin-Spin.
Chins need dust baths. They should not get wet, as their fur is very dense. Dusting not only cleans and dries their fur deep down, it makes them happy. Do not leave the dust in their cage all the time, they will poo and pee in it. Store bought dust, or sand, is not very good in quality. Some are even bad for the lungs. The scented dust baths are horrid. The best dusts are Blue Cloud and Blue Sparkle.
Like guinea pigs, the poo is a good window into the GI health of your chin. Poos are slightly smaller than guinea pigs, being the size of a tic tac roughly. They should be mostly uniform in color and not be squeezed off at the ends. Small poos can indicate a GI statis, bloat, or blockage problem which is very serious. Wet poos can be equally serious, indicating a bacterial infection, particularly giardia. Chinchilla poo doesn't really have an odor, so odor can be a bad sign as well.
I see from previous posts you have been looking into chin information since 12/15. It's a little sad you went ahead and got one and still haven't found much information in that time.
Here is some good nutrition info on a rescue site:
(broken link removed)
And Housing and Accessories page:
(broken link removed)
Her page also sells some excellent houses and toys for chins. Mine love the stuff I just got from her.
Other than that, I swear I'm going to put together a rescue friendly online supplies guide for chins. It's just a bit time consuming to do this considering I am only willing to do it at work because then I can get paid while you know, not working.