One thing that I don't understand is how the officer decides whether you can stay up to 6 months or not. I assume you must prove to them that you have ties back in the US.
Unfortunately there's no real answer to this question because the officers have a great deal of leeway when it comes to making this decision. One might ask for zero evidence and just let you in for six months without thinking twice. The next might ask for paperwork proving you have strong ties to the US (e.g. job, property, bank accounts) and question you to death. Then there's everything in between. They have the power to let you in for the full six months, let you in but only allow a shorter visit, deny you entry - or even ban you for a year (and yes - this applies to both Americans and Brits). I know this isn't a great answer. But it's reality.
As a rule of thumb, don't show up at the border looking or acting like you're moving (e.g. bringing a uhaul or a car packed with stuff is a very bad idea). Pack like you're visiting - since that's all you're really allowed to do. Bring strong evidence that ties you to the US. Have enough money in your bank account to support yourself during your visit.
You also mentioned attending school. If you're interested in doing this and want to take a course/degree/diploma that is six months or longer, you will have to apply for a study permit (once you're accepted by the school). You will also have to pay out of country tuition rates which are significantly higher than those paid by Canadian residents (i.e. Canadian citizens and PRs). If you haven't done so already, you might want to look into the fees. When applying for the study permit, you need to show a bank account balance that covers first year tuition fees, plus an extra $10K for first year living expenses.
Hope this info is somewhat helpful...