I think that most experienced riders will agree that power is the gold standard training tool, but the power realm has a steep cost of entry.
When I made the decision to become a better rider, my main metric was the distance ridden. After failing in an attempt at riding a century, I found that my ability to pace myself was lacking. I bought a simple hrm and over a few weeks identified a range of heart rates / efforts that I should be able to sustain. My next attempt at a century was a success. For me, starting out, the HRM helped by because my RPE was not calibrated; but my goals were purely distance, speed was secondary.
Fast forward a few years, now I have a more advanced HRM, better sense of RPE and still do not have a power meter. I do use the HRM data, but more for post ride analysis. I do little structured training, instead I pick a few days a week to ride with fast A group rides or I do a time trial or two on some local stretches of road. On hard rides, the HRM is running, but I ride at the pace the group dictates until the ride is over or I blow up. The other days, I ride according to how I feel.
I can recommend a few invaluable tools to the developing rider on a budget. First, push the limit, find a training partner or group that is faster than you are comfortable riding with, occasionally getting dropped is OK. Second, start logging data. Record your rides, times, miles, how you feel etc. To this end, a GPS device is a great and inexpensive tool. There are some online sites that have nice analysis tools and can track your times over stretches of road that you can define - there are also features that can even turn solo ride into a competitive event. Finally, invest the time in becoming better. Many on this site recommend that training at least 4 days a week is best for developing the physical adaptations beneficial to cycling.