That sounds right, actually. If you can stay on the saddle and put a foot down flat footed, it's usually a sign that your saddle is too low. You don't actually want you leg to be completely straight. You should have a slight bend at the bottom of your pedal stroke.

I'm guessing that your Roadmaster was a one-size-fits-some kind of bike and is likely too small for you. Putting the seat up really high will help, but when you have the budget it would be a good idea to get a bike made for someone your size. Make sure you aren't extending the seat post above the minimum insertion line. If your seatpost doesn't have such a line there's a good chance you are over-extending it. (I think you generally need to have two inches of seatpost below the top tube.)

If you're near an urban area with a decent used bike market, look for an old rigid mountain bike from Specialized, Trek or Giant. I'm a good bit shorter than you, so my size estimate might be way off, but I think you probably want something around a 21" frame for a MTB (though for a road bike you'd need something bigger).