Welcome.
That's a good question. I'm within an inch of your height and only about 5 lbs less. Unfortunately for me, there wasn't a "right" answer until I put some miles and time behind me.
I'd say stick with your Roadmaster until you figure out where your interests lie. In about 1000 miles you'll start getting an idea or two from boards like this and the folks you come across in your travels. That's about how many miles I put on a WalMart Mongoose MTB before deciding I preferred road biking and bought a used Giant OCR 2 that fit into my budget this Spring. If I had tried to buy a decent bike earlier (read anything other than a discount store bike) I would have picked the wrong thing.
Besides, if you decide to try your hand at working on your own bike, the cost of mistakes is lower.
There are some neat bike platforms out there to suit everybody; on-road, off-road, stunt-doubles, hybrids, recumbents, the list goes on, and you can spend thousands going and any direction.
I think it helped me to find and enter some of my local bike events just to see what was going on and what is available. Usually there are "charity" type events in many disciplines that have "novice" or "fun ride" groupings that let you participate without having to race the guy that weighs less than your left leg on a bike that weighs less than my cell phone and costs more than the car I drive back and forth to work.
It's all fun. If it's not fun, you're not doing it right.