Osirisdon -- I do just over 12 mi one way on my comute so I think 18 is doable with practice and training. You are on the right track to start slowly with one way trips and build up as you get more used to the distance. I'm sure you've already come across suggestions on how to break the trip up and get used to it. Many of those ideas will be very helpful to you, but pick and choose what works for you -- there are no absolutes in the commuting world.
On your current bike I would suggest using slick tires that are fairly narrow to reduce your rolling resistance. As for new bikes, much of what you choose will have to do with personal preference and your local conditions. If you ride gravel paths or really bad roads, you might want to steer away from roadbikes and consider cyclocross or hybrids. You will find tons of threads on bike preferences, in the end we each choose what works for us, based on what we can afford and what is available in our area.
I would definitely check out your LBS or even more than one to find a shop you like. As a relative newbie you will use them a good bit so it is worthwhile finding a shop that deals with commuters and can offer you good advice. Some shops seem so geared to the Lance wannabes or the mudspattered mountain bikers that they seem reluctant to take time out for the mundane commuter. You'll probably need stuff for your current bike so its a good excuse to hit a few LBS to see what sort of service you get and how hard they push their stock. If you don't feel comfortable with the shop move on to another.
As I'm sure you've already read, do lots of test rides to see how different bikes feel and handle. Use the web to double check the sales pitch and try to resist the urge to buy the first thing that catches your eye. What ever you buy make sure you look for dropouts to attach racks (since you will definitely want panniers or rack bags rather than a backpack for 18 miles). You'll want to make sure there are attachment points for a couple of water bottles and any other items you might want to tack on. Stems that offer multiple adjustments are usually easier to fine tune to your needs -- especially since those needs will change over the first 6 months of your ride as you settle in to the distance.
Remember that commuter bikes do a lot of work so they need maintenance and sometimes heavier components are a better choice than the lightest weight item. At 180 miles a week (if you ride the full roundtrip every day) you will be putting serious miles on your bike and need to outfit it accordingly.
On a final note you can shop around at places like Alertshirts.com and other online places for cheap polyester t-shirts and shorts, etc. to outfit yourself comfortably to lessen the cost of bike commuting. If you really get into it then you can always upgrade to a spndex wardrobe in the future. Even at this point I am quite a ways from wanting a spandex wardrobe (a point of view shared by many riding behind me).