Welcome to the forums!
You have certainly come to the right place as you will find all you need to know on budgie care here.
You are definitely on the right path to form a good and trusting bond with your budgie. The fact that he moves closer to you while on the cage is a very good sign and it means your budgie feels comfortable around you and is receptive to having a closer interaction with you.
You can use your voice to your advantage in order to further connect with your budgie. And this is done by talking and using a positive and encouraging tone to your voice and use praise words as a reward for good behaviour.
Generally budgies aren't that fond of being petted, so it's really important to read their body language and act according to it.
If you happen to hear the little warning chirps, you will know your budgie is bothered by it and he can show further disapproval by biting in return.
While your budgie may be receptive to petting now, that may very well be due to the fact that he is very young still and once he reaches his "teenage" phase, the chances are higher that he will not accept the petting.
Once your budgie fully masters the step up command and feels overall more confident, you can then move forward in training and starting to allow your budgie to have supervised out of cage time.
You will find all the detailed information and tips on how to tame your budgie by checking the the stickies here at the Training and Bonding section.
If you post a photo taken in natural light (no flash from camera) showing the whole beak/cere area, we can help you identifying your budgie's gender.