In the olden days, people would turn their collars and cuffs over when their shirts started to show wear. It's tricky to do and if you don't own a sewing machine, not at all cost effective. When I sold Men's Furnishings at Nordstrom, I often made the case that ironing one's own shirts was not all that frugal. Not nearly so effective as, say, brown bagging one's own lunch.
In conservative business settings, there is an advantage to presenting oneself in a crisp, professionally laundered shirt. Home washed and ironed shirts do not look or feel quite the same. Find a reputable laundry that offers good pricing and become a regular customer. Go easy on the starch, as heavy starch stiffens the fibers to the point that they break, causing fraying. Wear t-shirts, shower regularly and change as soon as you get home to maximize the possibility of wearing shirts twice. Shave your neck well to avoid sandpapering your shirt collars. Rotate your inventory so your shirts wear evenly.
Once you know your size and style preference, look for them at GW, consignment/thrift stores and estate/garage sales. If you know a bargain hunter with a good eye, give them a clear, concise description of your preferred shirt size, type, color and have them keep an eye out for them. If you set a really low target price, you won't be out much if they don't get it 100% right the first try or two.
Men's classic button downs haven't changed all that much over the years since the advent of no-iron cotton. Try not to buy poly blends. They tend to pill/yellow and generally look cheaper faster. Light colors are somewhat less fashionable, but tend to last longer, particularly if your skin is oily. Learn how to replace your own buttons and keep a sewing kit in your desk or briefcase for emergencies.
Final thoughts on cleaning business shirts at home, if you must: I have had good luck with a l-o-o-o-o-ng soak in "Biz", which seems to be tough to find these days. Oxyclean would be an alternative if you can't find Biz. Another trick is to spot treat with Zout and gently work it into the stained areas with an old, soft toothbrush.