yes, absolutely get fit. the faster the better... not doing so can lead to physical problems such as IT Band Ligament Syndrome... which makes your knees feel like they're being stabbed! I DID NOT get fit when I was new and am now paying the price! I have been professionally fit since and also have begun a stretching and strength training routine... both are helping tremendously and last Sat I was able to ride 59 miles... 2 weeks prior I made it only 14 before the knee was excrutiating... it's definitely worth it to pay for a fit so you don't end up with a medical problem...
how tall are you? Inseam? and what kind of bike? top tube lengths vary (Lemond runs long)... I am 5'7" but have a 30" inseam (short legs... family curse) and I ride a 49cm bike... I have a friend who is almost the same height and rides a 51 tho... so you may be right on! Good luck with it and keep us posted OK?
There is a fine line between "hobby" and "mental illness".