A bit younger than the children I work with (3-5 yrs) but here are a few thoughts.
Have you told him about the baby coming? I have often found children (especially the younger ones) react negatively towards mum with attention seeking behaviour around this time.
Even if you've not told him it might be that you've changed how you're behaving around him e.g. less boistrous or not picking him up as much and he's reacting against this as he isn't sure of what it means and is interpreting it as you rejecting him.
I would recommend having a chat with him about the baby coming, with a few suitably aged books to look at together. Talk about how you will still love him and love the baby too, how love grows the more we share it. Look at pictures from when he was a baby and talk about how much he's grown and changed. Be careful about emphasising what a big boy he is and how he doesn't need you as much now and the baby will need you more as he might react against this by becoming needier. If already toilet trained be warned that children sometimes go backwards when there's a newborn around. Talk about all the important ways he'll be able to help you.
Also make sure there's lots of time spent together without baby talk. Keep routines as normal as possible and don't feel you have to give in to his behaviour because of it being caused by baby coming.
For 3 yr olds I'd normally recommend a sticker chart with rewards which would probably not be right at his age. However you could have special stickers (shiny ones with fav. characters work best -I find Peppa Pig to be the most enticing) which you'll give him if he does what mummy says or eats or plays without throwing things. Have some pictures (happy mummy) to represent these things somewhere he can see with the stickers to remind him what he'll get them for -when he does wrong you could draw his attention to them and say how sad you are he didn't do X as you'd love to give him a sticker, maybe next time! And also point to them if you see him about to do something e.g. picks up food to throw -point to the picture "remember I'm looking to see you finish you lunch tidily".
When he does the right thing make a big fuss about it. When DP comes home make a big fuss of how good he was and how he's got a sticker for X even if he has done lots of things wrong emphasise in front of him what he has done right and get dad to praise him! (Later tell of all the horror of the day -not in front of him!) Do not remove stickers for later bad behaviour. Even if he has done something wrong, he has still done something earlier right and that's what you want him to focus on.
Try to avoid rewarding his negative behaviours with attention. If using naughty step/time out be consistent and keep verbal/visual attention to a minimum. Do not shout but use a plain calm (robot) voice to state what he has done wrong and what the consequence is. Do not get involved in a discussion and avoid getting sidetracked by secondary behaviours (e.g. screaming after you've put him on time out). If he shouts no, ignore it and just put him back on time out, perhaps restating in the robot voice what the behaviour and consequences were.
Hope these ideas are of some use to you. Feel free to ask for more advice but hopefully someone else will have more experience with this.