I am no expert on training, but I'll offer my own experience for what it's worth. When I first started road riding as an adult in June of 2006, it soon became abundantly clear that while I wasn't in the worst shape, I struggled with hard efforts, e.g., going "fast" and hills. So, after riding through the summer and fall, I spent the winter on base building in thrice-weekly spin classes. I kept my heart rate at a moderate level and avoided any kind of max effort. I also worked on core strength and flexibility through a regular yoga practice. My spring, I was in MUCH better shape to start working on speed.

Like you, I wanted to be faster so that I could comfortably ride with friends. I've never been one for intervals, but I became a regular attendee at our club's weekday training rides. Those rides are done in a paceline formation at a hard effort. Assuming I could hang with the pack, I would take my turn at the front of the line and that would amount to interval training. In time, I definitely got faster, but it was gradual. By mid-summer, I was able to keep up with most of my friends. It wasn't until the following year, however, that I could do so comfortably over most terrain. I also got better at climbing with practice, but that took even longer.

So, based on what you've shared about your own experience, I have to wonder whether you need to work on building your aerobic base before trying to tackle speed work. I understand your impatience, but you might be better off putting your speed goals aside for the time being and simply work on your endurance. But like I said, I'm no expert.