There's basically three kinds: tiny plastic rubbish ones, regular non-programmable ones, and ones with a computer on board that allows for fancy embroidery etc. You need the second kind.

Stay away from the <$100 models (unless it's a massive discount!) because they don't tend to handle anything well and definitely won't cope with nylon. You can buy refurbished models much, much cheaper than new ones, if that helps. I have a Pfaff, which is good, and I used to have a Singer. Janome and Husqvarna are also good. Sewing nylon is tricky but it's more up to the person adjusting the machine than the machine itself.