What is a realistic "base" for me?

Joe,
What are your cycling goals? For instance are you after general recreation and fitness or perhaps you want to do organized day tours and things like century rides or charity rides (e.g. 50 to 100 miles with food stops along the way) or do you have an interest in competing in some form of cycling?

The answers to those questions (and they may change over time) helps define 'base' training. IOW, base training for a racer basically is a foundation of endurance and aerobic fitness (sustainable power) that represents a foundation on top of which race specific fitness like hard short intervals and sprinting is added. For a fitness oriented cyclist all riding may be considered 'base' as it's just getting on the bike and challenging your body to adapt to longer and or quicker riding but there's no point in the year where you'd necessarily switch to things like gut busting one minute hill repeats or structured sprint workouts. Similar story for someone interested in one day sportifs and century rides though they may do some specific hill work or other things to address the challenges of longer days in the saddle.

So basically figure out what you'd like to get out of cycling and it'll help you figure out what you need to put into it.

But as a starter, do what you've described. Ride more, ride higher paces (for sustained efforts of 10 to fifteen minutes or more as opposed to short crazy hard make ya puke style work) on days when you feel good or have some nice open roads to work with and your basic fitness will improve which hopefully is one of your goals regardless of where else you'd like to take your cycling.

Good luck,
-Dave