Experimenting with strings is like opening a can of worms. Once you graduate from Prince syngut you will never go back, and it gets a lot more expensive and can become like an obsession trying to find the right string for you and your racquet.
First, the easy part. The "16, 17, 18" is the gauge, or thickness, of the string. The bigger the number, the thinner the string, the more power it creates, and the easier it breaks. If you are a big hitter who tends to break a lot of strings, you may want to consider a thicker gauge string.
If you go on a tennis wholesale equipment store website like Tennis Warehouse and look at their selection of strings, you will be overwhelmed at the sheer number of 1) manufacturers and 2) types of string, but the only way to start researching is to dive in and start reading. If you can set aside some money to try a few different strings over a couple of months, I recommend doing that. Play with each for a few weeks and give it enough time to settle in so you can truly get the feel of each as it passes through the stage of relaxing in tension a bit. Try hybridding some strings (a different type of string in the mains than the string used from the crosses). Try a good polyester string, a good synthetic, a multifiliament, and even a natural gut if you can afford it, maybe a couple of the better known of each.
"Players" or "pro" strings are popular but may not necessarily be best for you. Not everybody has the game to play like Nadal, but Tennis Warehouse sells alot of Babolat RPM Blast string--some like it, some SAY they like it because Rafa uses it, and some cut it out and toss it in the can because it hurts their shoulder after a weekend of playing with it because they aren't it shape to handle it. You need to take this into account when researching and testing strings and find something that is a good balance for your own needs--whether that is control, power, extra spin, or durability.
As for tension, that is something you simply need to experiment with over time and find a balance with. The same string plays completely different at 62 pounds than at 50, so if you hear great things about the latest poly string and try it strung at 60 pounds and it feels like garbage, keep in mind that it may be designed to play at a lower tension.
I can't tell you all of the most popular string brands--I have no experience with Wilson brands, e.g., but most any Luxilon Big Banger, Babolat Pro Hurricane Tour, any Babolat natural gut, Solinco Heaven Tour Bite....these are all excellent strings that pros play with. I've strung racquets with all of them in hybrids and liked the feel of playing with each.
If you want a cheaper alternative to natural gut, Gosen OG Sheep Micro is quite inexpensive and works nicely.
One final piece of advice--do NOT let a big box store like Dick's Sporting Goods or Sporting Authority string your racquet if you can help it. Their racquet stringers do not have to be USRSA certified and in nearly all cases, are not, and likely don't even play tennis themselves. It's worth trying to find a local Racquet Stringers Association certified technician to string your racquet, even if it costs a bit more. They can offer you invaluable guidance and advice on strings and tension, etc.
For me, the key indicator is when I have to start sliding my dampener back down or adjusting my strings every several points. 
