Is he being agressive or not?

Hi all new here & looking for some tips, 2 days ago we re homed a 1 yr old staff & is still very early days but am mostly very pleased with his behavior. He was spayed end of june & naturally still shows alot of signs by sometimes hugging mine or my sons leg, my only concerns are he is trying to dominate me or my boys (age 14 & 11).
Previous owner was a lady with the husband working long hours so think his behaviors are continuing here as he reacts to my wife's instructions well & does not try to dominate her or my daughter age 10 but sees males as a play mate & not a leader.
He continues to mouth/nip at trainers & ankles to get attention to play & when is told a firm "no" he shows teeth/barks & air snaps while bouncing around. I have read so many ways of showing him who the leader is but want to be sure I get it correct, at the moment I am pushing on his shoulders when he starts to nip until he submits by laying down with a firm "no" then take him to his bed when I try to get him stay.After doing this throughout the day this evening after being put in his bed he ran past me to the garden turned to face me where we held eye contact for a good 2 minutes until he laid down but as I approached he took an aggressive stance then wanted to play but I ignored him.
He has been walked once yesterday twice today (2 to 3 hr walks) & is very good on the lead/around people in public & other animals it is just this one issue then he would make a superb pet.
Any advice would be good, thanks in advance.

Sounds more like play behaviour to me. At the top of the forum there is a link to the website. There you will see a basics for new owners section that gives tips on the mouthing problem as well as recognizing dogs body language. I would post the link for you but the site doesn't work for me at the moment.

Sounds like play/boundary testing! Start as you mean to go on, lots of exercise and 2/3 short 10 minute training sessions a day, each member of the family should do a training session each to ensure he's listening to you all and you're all being consistent in commands.

My dog was a stray and knew no commands; I taught her sit/lie down/stay/wait/leave/drop/come and that no teeth belong on skin as quickly as possible, but she loves learning so she now knows roll over/play dead/paw/high 5/wave etc as it keeps her brain ticking over learning new tricks. I would print off some positive command training sheets online and all follow the same one, teaching one command at a time until it's mastered and then moving on. Cheese usually helps though Biscuit got over excited by cheese so I taught her with a lower value training treat.

You don't need the dominate him by showing who's the leader, and to be honest pushing his shoulders and making him lie down is still giving him physical contact, positive or negative contact doesn't always matter. Turn away and retract all interaction, use a firm "no" only when it's REALLY needed, if you say it all the time it will lose meaning. I wouldn't intimidate him with eye contact either. I've never used dominance and my dog was very aggressive when I took her in, she listens to and respects me because I'm clear, confident and consistent. Not because she fears me, which is all forceful techniques do;scare. Which produces an unbalanced dog.

Thanks Rachel, am doing regular training with him & is doing really well. he understands sit/paw/lay down & leave at the momment & am introducing a clicker with his training.
His behaviors are becoming slowly less & less, the nipping at shoes in the garden has nearly gone now, he still air snaps occasionally when over excited playing & am convinced his humping will also vanish as he is still only 4 weeks after the op but overall a very loving & caring dog with potential to learn so much more.

Wonderful news hope he continues to do so well. My dog also tries to hump people and she's a spayed female, she did it a lot when she came out of kennels. From my observations I think that she does it as tension release, when she's over excited it's her way of releasing that excess energy. I've never seen it as a dominance thing with my girl, though it can be, it can also be a lot of other things well done with your boy!