On being classically fashionable that's easy. Think of the classiest person you know. Let's say Audrey Hepburn. If she were around today, what kind of outfit do you think she would wear? Then modify your outfit to make it up to standard.
The budget, however, will make shopping seem daunting. But it's not. Our favorite option would be shopping vintage. Don't worry about the fit so much as you can always take them to your seamstress to have them altered to a more modern fit.
If your not that all enthralled by the thought of hunting through racks of pre-warn clothing, where do you live? If it's in a city you can always go to department store outlets like Nordstrom Rack, Saks Off Fifth, Neiman Marcus Last Call, et cetera. Be wary of chains like Forever 21 and Charlotte Rouse no matter what anyone tells you.
Stores like J. Crew and Banana Republic are great too, seeing as they almost always have sales.
You may want to try ShopItToMe. You pick out your favorite brands, stores, sizes, and price ranges; and
everyday they have complied for you exactly that.