One thing you got going for you, you already know how American’s talk! … lol …
No experience w/buying in CT and moving to IN. But if you buy a car in another state and then move to California, you will have to pay sales taxes in the other state when you buy the car, then pay them again to register the car in Calif. Calif politicos do that – presumably at the behest of Calif car dealers – to discourage residents from crossing the border into another state to buy a new car. Folks might otherwise do that for a variety of reasons, including reduced price b/c of lower state sales tax, or the other state requiring fewer emissions components. I suggest you wait to purchase your car in IN. I doubt among common seen cars on the road there’s a single make/model you can buy in CN that you can’t just as readily buy in IN.
As you probably already know, each state in the USA has its own vehicle rules. To know for sure you’ll have to research the rules in each state, or hire a lawyer for advice. In general the USA is more like 50 individual countries each with their own rules and laws, than one country with uniform rules and laws throughout. .Just a heads up, so you don’t fall into that trap.
Buying a used car in the USA. Easiest method imo is to buy from a rental company sales lot. Hertz, Avis, etc all sell their rental cars when they get 3 to 4 years old. Competitive pricing, cars have been well maintained. The only downside, you’ll have to settle for an automatic transmission. If an auto trans Subaru in the 2017+ vintage is ok by you, I think that’s your best bet. Other methods are from a dealership, or used cars advertised in newspapers or on the internet (EBAY, Craigslist, etc.). If you choose one of these two methods, good idea to ask someone local who has done it before advise you. Good idea to visit the state DMV office before starting this process to find out what you need to watch out for, forms you need. Some states require the car pass an emissions test for example, before they’ll allow it to be registered. I expect you already know that you want to make sure the seller has a right to sell the car, so you are the only one that owns it after the sale of course. The DMV will show you how to make sure.
No idea bout financing cars, I’ve always purchased cars w/cashier check from major bank in full amount. Suggest you do that if at all possible, makes the process much more simple.
American’s often used a book called “Consumer Reports Guide to Used Cars” to decide what make/model/year to look for that best meets their needs. When buying a used car, good idea to hire your own inde mechanic to first do a pre-purchase inspection. $100 or so, money well spent.
Suggest to fly from CN to IN rather than rent a car and drive. First of all, you may be driving on what you think is the wrong side of the road. Not 100% safe until you get used to it. Compare driving vs flying prices at least.
If you have access to back issues of the UK magazine Practical Classics, try to find the article where Sam Glover (one of their writers) flies from the UK to Southeast USA, buys a Corvair, and drives it across the USA to Los Angeles. Pretty good explanation of the issues you may run up against.