Stevens 200, H&R Handi-Rifle, Mossberg ATR100, Marlin XL7, Ruger American, Savage 111, Savage Axis (aka Edge.) Alll of these are available new for less than $500. Some of them are quite a bit under $500. Some of them will include a sope, mounted, for that price. The scope won't be top quality, but usually it will do its job well enough. .270Winchester is certainly a good calibre choice for deer and moose.
If you go to the used market you can find the above selection a bit cheaper and also find nicer rifles that are more expensive new. If you aren't confident of your ability to judge the quality or condition of a used rifle, go to a reputable dealer. One of our site sponsors, Trade Ex Canada (T.E.C.) in particular seems to always have a large stock of used guns, usually classic older styles, and their prices are reasonable and they have a very good reputation amongst the Gunnutz for their service and for not overselling the condition of their guns. There are other good dealers on here, too, but T.E.C.'s website is particularly good because there are so many guns, all with pictures.