Hi mgrgrl! And welcome to the club. :)
First of all, before you worry about standing up I'd recommend that you get VERY comfortable using all the controls-- clutch, brakes, and throttle. Shifting, stopping, and accelerating should all become second nature-- you won't even be thinking about it. Practice corners, set up some cones for figure 8's, and do some drills. (Also spend some time just playing around!)
These exercises will help you become more comfortable with the bike, and THEN you can think about standing up while riding. As KDXgirl mentions, once you start standing up more, you'll probably want to adjust the controls so they are are more comfortable in a stand-up position. Standing up allows the bike to move freely underneath you, lets your legs act as more "suspension" for soaking up bumps, and allows better overall control of the bike.
Sounds like you have a pretty decent starting bike. The TTR125L and the CRF150 are good beginner bikes, but you might find them a bit small, especially after you get some experience. Other options for trail riding are the CRF230, Pampera 250, or even a KDX200. If you're thinking about doing motocross, you may want to look at a KX100 or any of the 125's.
For now, have FUN! (And make sure you get all the safety gear-- helmet, boots, etc.)