Should I replace all four tires on my car, or is it ok to move the two from the back to the front and buy two new ones for the back?

you should keep the best tires on the front. If you blow out a front tire you are more apt to loose control of the vehicle than if you blow out a tear tire.

amazing Discount Tires here in Dallas, Tx told me the exact opposite.

Your front tires are for steering, and many cars have front-wheel drive, as well. That is why you typically want the best tires on the front, if you haven’t been rotating them every 5–7,000 miles, as recommended. If you have 4WD or AWD, I’d still want the best tires on the front; but if you have rear-wheel drive, it depends on a number of issues, such as the driving conditions and just how bad the older tires are. If you can possibly afford it, the best bet is to buy all 4 and rotate the new set regularly.

only replace the ones needed