I would generally second what Carrier and Rainboe are saying. While you're training in SEP you don't need better hearing protection than you get from a decent set of David Clark passives, like the 13.4s or the 10-30s for example. Where it becomes nicer to have the ANR sets like the Bose is when you either graduate to noiser aircraft such as twins where you need better noise reduction or if you're flying in a single all day every day, for example if instructing, where it allegedly reduces fatigue noticably.
As another note, I don't actually recommend the DC ANR set (the X-11) , it doesn't seem sturdy enough, the clamping around the head is not even enough, and anecdotally it doesn't cut as much noise as the Bose. This is from a happy DC H10-30 user. See if you can test fly one first, and check both active (ANR on) and passive (ANR off) performance. There are plenty of ANR headsets which don't work well at all when the batteries die.
My opinion: Get the best and most comfortable headset you can afford now. When you get that first job flying all day, then it is time to hit the bank up for a personal loan for the expensive ANR set. Second-hand DC H10-30s are really cheap and easy to get, then you just buy new gel-seals and they're as good as new.