Welcome to the Chinchilla Club and congrats on your new chin. I have a male chinchilla (Kulu) that I purchased from a breeder at 3 months. Yours has a very nice looking coat compared to his at that age. Kulu grew very rapidly for about 6 months and has pretty much leveled off at about 470 grams and now has a beautiful coat and form. An average male chinchilla weighs 500g but they can be quite a bit smaller depending on breeding. I strongly recommend charting your pet's weight once a week starting immediately. You can get a small travel cage and weigh him on it. This comes in very handy if you suspect your chinchilla is sick. One of the most common questions that are posted here is "Is my chinchilla sick?" This will make it easy for the vet to answer that question since chinchillas hide their sicknesses but usually go off their food when something is wrong. Oftentimes the anorexia is worse than the thing that causes it and is often fatal when it goes unnoticed. Monitor your chinchilla's food and water intake every day and you'll avoid problems if they occur.
Here's a list of 10 things new owners sometimes have issues with. I know I've made similar lists before so it may differ since I'm going off the top of my head:
1. Dust baths should be given no more frequently than every other day to prevent dry skin.
2. New chinchillas should not be allowed to roam outside of their cage until they are bonded to their owners. A big part of this is when the chinchilla allows you to pet it and does not jump away, and/or will typically come to you for attention while interacting through the cage. Failure to observe this often makes them very hard to tame.
3. On the first few times you let your chinchilla out to play you should do it in a room that has been made safe. Usually this is the bathroom. Chasing your chinchilla to catch it will cause it to dislike you and will lengthen the bonding/taming process so try not to let it escape into a room where you must chase it.
4. Many new owners will give their chinchillas diets marketed for chinchillas that cause health problems. Anything from tjschinchillasupplies.com is usually high quality. They make it easy to select food 'cause I don't have to list what is good and what is not and tell people where to get it. I recommend going with Purina Rabbit Show at least until your chinchilla is 8 months old. This will help your chinchilla grow. They are typically full grown in a year. (Remember to mix diets over a week when changing diets and do not change the diet until at least two weeks after relocation)
5. Sometimes chinchillas are fed treats that are unsafe or too much of a treat that is considered safe and sometimes chinchillas die from this. As a treat give no more than 2 raisins in a day and only if the stools are normal. Sometimes a raisin will cause loose stool in younger chinchillas so see how he handles one. Do not give treats until about two weeks after you take him home because they are typically stressed from relocation and this causes bowel irritation. Restricting its diet to hay and alfalfa-based pellets is actually best practice. Raisins should only be used as aids for taming and can be chopped into smaller pieces. That is my personal opinion based on my own research although others may differ.
6. Do not use wire shelves or wire hay balls or hay feeders in a chinchilla cage. Injuries and deaths get reported from those things fairly often here.
7. Do not put items made of plastic in the cage. Plastic can be dangerous in several ways. Same thing with cloth items. (Artifical woven "fleece" is an exception only if the chin does not have a habit of eating it). Bowel obstructions from cloth and plastic are fatal if they occur. Sadly we may never know how common this is because death from bowel obstructions is difficult to positively diagnose. Most chins with that condition will probably never be x-rayed or necropsied before they mysteriously stop eating and die. Be very careful about materials your pet chews on.
8. Do not use a chinchilla ball if the room temperature is much above 72F. When you use your chinchilla ball make sure he does not chew it and make sure you check him for overheating every 5 minutes. Failure to follow these guidelines has lead to numerous deaths as chinchillas are easily overheated and chinchilla balls do not have adequate ventillation. Some say to not use one but I use mine understanding the risks.
9. Try to keep your chinchilla's room's temperature below 75F. If you live in a warm climate and your chinchilla is used to higher temperatures keep in mind that much above 85F can be fatal. For chinchillas used to living in lower temperatures 75 can be fatal with physical exertion. Never allow your chinchilla to go where there is direct sunlight.
10. Always keep water, hay and pellets available at all times. Always have wood in the cage for your chinchilla to chew. Chinchilla's digestive systems are sensitive and going several hours without eating can potentially cause big trouble. Without regular access to hay or wood chews tooth overgrowth may occur that is often fatal or very difficult to treat.
Also do not let your chinchillas chew on power cables or get near them. Death from electrocution and burns from this is not that uncommon. As you know they can get all the way to the conductors with just one chomp.
Chinchillas have sensitive digestive systems, prefer cold climates, and are easily stressed. However in practice I find keeping chinchillas to be very rewarding in spite of that and these things are quite manageable when you think ahead.
Also I wanted to note that my chinchilla is always on the move and does not like to be held still for much more than 10 seconds. That is typical chinchilla behavior however the more you work with him and hold him (once he has bonded with you) for short periods every day you'll see him get calmer. Also they do mellow out some with age. He will allow me to hold him for several minutes now (at 10 months) although he prefers to roam around.