You already mentioned a good description of what a good "base" effort should be- you push yourself until you're a little out of breath, and can ride a couple of hours that way. It should be a pace where you are breathing harder, but you have very little, if any, lactic acid burn in your legs.
Honestly, if you're somewhat new to riding, the more you can just get out & ride (or stay in and ride!), the better! I think that putting a strict timeline on "base building" is a bit overrated- you should train that way on a regular basis, but if you feel like riding harder sometimes, then by all means, go for it!
Really the point of base training is to get you ready to spend longer amounts of time in the saddle- your muscles adapt to exercising for extended periods of time, your body becomes accustomed to digesting/processing food while you ride, your seatbones toughen up... All of this can be useful even if you're not racing. If you want to be able to have fun on longer rides, then it makes sense that you should get your body used to these things in order to keep you more comfortable.