Ensure you have boundaries in place.This is so so important. Especially if it's the first relationship both of you have had since you split up with your children's other parent.
Do you feel your partner interacts with his ex appropriately?
Do you feel you interact with your ex appropriately? Ask your partner this too.
From experience, sometimes it isn't until someone else comes on the scene that the parent realises that their interaction with an ex may not be very constructive. For example, I had a friend who met her now fiancée about 10 months after he split up with his son's mother - however, because nobody had said anything to him to the contrary (and he was desperate to see his son) the fiancée would regularly go to the mother's house and stay for hours at a time. On paper it looked perfectly amicable and in fact, very admirable, but the reality was that when my friend met his son (and son's mother) about 4 months later, the reality was that the mother was still deeply angry at my friends fiancée and even though he was round there to see his son, he'd often get dragged into snippy arguments in front of the little boy. It wasn't blazing, so nobody felt they were acting inappropriately, but my friend, as an outsider could see just how destructive them playing happy families was. Because her fiancee's ex wasn't being honest about how she was feeling, it would come out in waves and always ended up setting her fiancee back as he was trying hard to just be there for his son.
I don't know if that makes sense, but what I'm trying to say is that blending a family is about sticking to your principles and beliefs about parenthood but at the same time accepting that "fresh eyes" can sometimes help.
I'd say 3-6 months would be a normal time to meet a partners DC (really depends on the amount of time you spend together tbh) - I would suggest you guys seek to meet each others children first, before you try to get them to meet each other, especially if the children are only children and haven't had to experience vying for attention. Get to know the kids seperately, talk about your own kids, gauge whether the kids want to meet and go from there.
As for dealing with exes - there are no hard and fast rules. Some exes are fantastic, some are nightmares. Talk to each other about your relationship history - you can get an idea of the ex partners personality from conversation, but I think if your new partner is particularly disparaging or disrespectful toward his ex, you'll have a job on your hands because it indicates there is a lot of animosity either clearly out in the open (not good for the kids) or under the surface (not good for anyone). But that is where boundaries comes into force again - you aren't your partners therapist - if he's got a lot of issues, he needs to talk to someone other than you about it, whilst knowing you are there (I made this mistake, and it bit me in the arse!) - but vice versa, if you've got a lot of unresolved issues with your ex, seek advice on how to deal with your past before bringing it into a new relationship.
Basically - the past is the past. You both have children to other people than each other. You can't change that, and you have to contact them/be civil/work together. If either of you are hung up on the past, you need to resolve those issues first to give yourselves a better chance of working well into the future and establishing boundaries for yourselves and your children.
Sorry, I'm wittering away...blame the heat!