How do I get my whites perfectly white and STAIN FREE?

I work in the front of house at an upscale restaurant. I only get 2 work shirts so I have to do my laundry every 2 days. I HATE laundry, so I tend to be kind of lazy at it to be honest. Anyway, I noticed that although my shirts LOOK to be clean when I take them out of the dryer, upon closer inspection, there are grease stains, soup stains and general dingy-ness. I have in the past used bluing to get a whiter white and also shampoo around the collar but the worst parts for me tend to be around the sleeves. My washing machine isn't great and I can't afford to get a nicer one any time soon. I usually use warm-hot water (depending on what my washer wants to do that day) and TONS of bleach. What else can I do to ensure perfect work-ready whites?