The single most empowering thing you can do at the moment is to suspend any decisions. Please don't tell him that you can forgive, or that you have decided to commit to this marriage. This isn't game-playing, it is the truth. You might feel enormous relief just now that it appears he has chosen you and your DCs, but you simply cannot know whether this is too big a hurt to get past, or whether you are capable of it.
In terms of what needs to happen now, he should cease any unnecessary contact with the OW, giving you enough information to support your belief that this is over between them. In an ideal world, he should not work alongside her any more and so he should start making moves now to change jobs/roles. Sadly, upon discovery, many of these relationships start up again, particularly when the parties still see eachother through work. This relationship only ended because you found out and it probably didn't run its course.
We are all different, but if I hadn't been convinced of my H's sorrow and genuine remorse in the initial aftermath (it is unmistakeable from the sorrow of being caught) I could not have attempted recovery.
I wouldn't rush to counselling at all in these initial post-discovery weeks, mainly because it is nearly always the case that the betrayer is still lying about - and sanitising - their own role in events.
In these early weeks, you will perhaps also be feeling very unsafe and frightened. Your whole world has been rocked and it will seem as though a seismic event has shattered your very existence. You will also feel massively insecure about the continued and daily threat of the OW.
Amongst the many questions you will have about how the affair started, who initiated it, who knew about it and how frequently/where they met up, the most pressing question will be "why?"
You will need a teflon skin if there is any tendency on your H's part to blame you for his behaviour, or to blame the OW disproportionately. Affairs happen in good marriages; they happen in bad ones, but adultery is always wrong and the unsighted and deceived cannot and should not be blamed for its occurrence. You need to distinguish between accepting responsibility for any problems that might have existed and the response to those problems.
If he does go down the blame route and claims marital dissatisfaction, your response should be that the adult resolution would have a discussion with you - not an affair.
It is not an easy journey and male infidelity in a marriage of under 10 years' duration is not a good portent for the future.
Once you have sorted out the major questions and got to a place of safety, take the counselling route. You might find it better initially if you each have therapy on your own.
Infidelity is all about the person practising it and your H will need to resolve why he felt entitled to risk not only his relationship, his family's security but also your health. It nearly always emerges that infidelity is yet another example of extreme selfishness on the part of the betrayer and that this selfishness has always blighted the relationship - and will blight any further relationships unless it is resolved. Your therapy will be about the choices you have open to you, whether that is finding a way to live with this, or leaving the relationship.
Now that you are sighted about the infidelity, you have more power than when you were being deceived. The worst (although it won't seem like that) is over, because you know what you are dealing with now. What you won't know yet is the extent of the deceit, or the full details.
I always recommend creating a timeline for yourself, starting with the last time you felt joyous and happy about life. Cross match your feelings and inner dialogue with when this relationship started (including the pre-affair build up) and you will probably see that you have been suffering for far longer than this affair's active phase.
That is now over and you have got the power back to determine what, if any, marriage you want for the future. It is a once in a lifetime opportunity to get the life and/or marriage you have always wanted and deserved. Don't squander that opportunity, whether your choice is to heal alone or starting a process of forgiveness.
Remember that forgiveness is very much a process. It cannot and should not be given instantly. It can only be given if someone is genuinely sorry for the terrible hurt and it is only worth giving when you know exactly what it is you have to forgive. Above all, it has to be earned.
Do keep posting, as there are so many of us on this board who have been through this trauma and can help you.