Measuring Training?

If what you want is to measure how hard you are working, you have three choices, in progressive usefulness and cost. First, you can buy nothing and go by your perceived exertion (RPE). Second, you can spend less than $50 and get a HR monitor. You don't even need one strapped to your bike. You can get the chest strap and a HRM that you wear on your wrist. Third, for $600 (Polar) to $3,400 (SRM Pro) you can get a power meter. There are training programs designed around all three measures, but the essence of all training programs is that you do high-intensity rides 2-3 times a week, with a recovery day following each high-intensity day. Riding every day at a steady pace won't result in much improvement in your pace or your fitness. So as to not be anti-social, you can get in your high-intensity work on group rides by charging hills and going hard into the wind, then backing off and allowing the group to catch up on the flats and downwind sections. Most groups are perfectly happy to have someone go to the front and pull in a strong headwind. Andy Coggan is the Training Program Guru of the Western World. See his article (Training and Racing Using a Power Meter: An Introduction) for a training model. While this article is primarily targeted at those who have a PM, he correlates power with RPE and HR numbers.

Here are a couple good ways to monitor/measure your increasing fitness without spending more money:
1) pick a specific 20-30m route to ride once a week/month and time yourself on this route. Try to set a personal best time each time you ride it, and keep track of all your results (including weather/wind conditions).
2) try to stay with the group longer and longer each time before you get dropped. Don't pull at the front at first, just sit in at the back. Before long you'll surprise yourself by hanging on for the entire ride. After that, try to rotate with the group to take occassional *short* pulls at the front.

There's absolutely nothing wrong with trying to stay with the faster riders in the group. That'll help push you to become faster and is the crux of bike racing. Learn to draft well and ride smooth in a paceline, and you'll save a lot of energy for when it's your turn to beat the wind for the group. Hang on to that wheel as if your life depended on it, and good luck.