You can obviously check in at any T3 or G, but I'd just check a bag closer to whatever gate I was leaving out of so there is less movement of my bag to get lost.

If I take BART to the airport, I always sit at the front of the train and just get off and walk to G security. Lately G security has been so empty that you walk right up to TSA Pre agent. Then I just take the walkway to T3. The AirTrain can be so slow feeling at times.