Replacing Alternator...which one to get?

For 160, I would. I think I'm going to get a 130 amp and I'm going to upgrade the wiring. Americanmuscle has some upgraded wiring and the alternator your looking at is definitely cheaper than AM.
PA Performance Mustang Alternator - 130 Amp (99-04 GT) at AmericanMuscle.com - Free Shipping!

PA Performance Premium Power Wire Kit (86-04) at AmericanMuscle.com - Free Shipping!

The stock alternator should be 130 amps, so yes that would provide more juice. However, you should normally install a higher amp fuse and proper wire to handle the extra ampacity. You also shouldn't need a larger alternator unless you have a huge stereo or some other huge aftermarket power draw (running hydraulics at all 4 corners?).
That auction doesn't seem to list a name brand. I'd be wary of buying such a part from ebay, even if they do state there is a 1 year warrenty. Think about trying to collect on said 1 year warrenty... Are you really going to yank the alternator, pay the price to mail the old alternator there, hope they are willing to replace it... and then have it shipped back? Personally, I think the cheapest, lowest quality junk you'll ever is exculsively sold on ebay and they never tell you the brand of it. I'd either buy a ford/motorcraft part, or if that was rediculous, I'd go with the local parts store part that has a lifetime warrenty. Then, if the new alternator ever does break, you can run to the parts store, swap it out in about 15 min and be on your merry way.
Just my opinion from my experience.

Alternators only produce MAXIMUM output at higher rpm's. When you are idling, it will NOT produce 160 recharge amps. At idle, the alt will probably be at 20% output (in warm weather), which is enough to cover your headlights at best. If you want 160A instead of the stock 130A it will ONLY produce that additional current at MAX operating speed. Which means your engine will have to be spinning at roughly (guess) 3500+ all the time to see that 160A rating. You do not need a bigger alternator unless you have some rediculous ignition system, bigger aftermarket amplifiers, fold down tv screens, or a refridgerator. You get the idea. You will not gain anything with a 160A alternator. Go with a reman stock unit. OE+ makes a good alternator.

Go to your local parts store and buy a replacement oe alt with a lifetime warranty.... No reason to spend big money elsewhere. Plus with a lifetime warranty, you only have to replace it once.