Does the ANR only cancel out the noice inside the cockpit, or can it also reduce radio static?
Only the former.
"Radio static" is just a crap radio, or a crap intercom, or both.
At my school I fly 2 aircraft which have terrible radios, with a lot of static just on the intercom. Would the Bose A or X reduce this? If so it's probably worth a punt.
A good headset will always help you hear properly though, and will save your hearing too. Obviously I can't tell you what you can or can't afford, but if you e.g. plan to later join a syndicate (which, apart from outright ownership, is generally the only way to go long-term, since rental is usually an expensive way to fly garbage) then a decent headset will really stand out.
Plus they are much more comfy
I have been told by a few people I know well that while the bose-x and the LS Zulu are comparable, the Bose A20 is well above anything else. I have just ordered one (aircraft powered but without the Bluetooth gimmick) from the USA; some firms out there are offering a $400 trade-in on a bose-x which is more than one would get on Ebay.
One interesting thing about the A20 is that for $49 you can convert the aircraft powered (single Lemo plug) version into the standard twin jacks, which is useful if one wants to use such a headset in somebody else's plane. With the old X the only way to do this was to change the whole mike+cable assembly which was about £140, years ago.