Welcome to SBW!
Your acquaintance is correct in way, but at 160lbs, you won't have to worry about being too heavy for any bike out there. Now, if you were 325 and wanted a Ninja 250, that would be a different story.
Brand new rider? As in never been on a bike before? If so, get thee to a beginner's rider course before you do anything else. At the very least, have an experienced friend, one of the more mature, responsible ones, give you some instruction on how to ride. Getting instruction from a motorcycle sales guy as you leave the dealership on your new bike is not a bright idea.
As for a first bike, you might not like my advice. I always suggest that new riders start out on the dirt, as in with a dual-purpose bike. There is no better place for a beginner to learn balance, turning, shifting, braking, throttle control, etc., than on the dirt, for obvious reasons. An added bonus is this method of entry into motorcycling is relatively inexpensive. You can find a good used dual-purpose bike for about the same amount of $ as you're likely to spend repairing broken bits on a new sportbike should you go down on the street. I'm not saying you will go down, but just giving you something to consider. Once you feel comfortable on the dirt, you can move up to street riding. You'll be doing it on a bike that you're comfortable with, and it will make for a more enjoyable experience.
If you just have to have a sportbike, or don't have access to off-road riding areas, then it would be best to start off with something in the 500-600cc class. Remember, the less plastic it has on it, the less costly the repairs will be. Even used bikes in this category, which is what I suggest, have enough power to get you in a world of trouble. Respect is mandatory.
When considering the cost of getting into riding, don't forget the cost of gear, as many people do. You should have, at a minimum, a full-face helmet, riding gloves, armored leather or textile jacket, and over-the-ankle boots to get started. Having armored pants, instead of jeans, is also a smart idea.
That's all I have time for at the moment. Others will chime in with good advice. Good luck and keep us posted.