It's worth talking about expectations of how involved he will be with the DC, and examining how you feel about that. I found it really hard when DP started to transition from "family friend who DS occasionally saw but mainly as a playmate" to "possible future father figure" and was around a lot more and naturally on occasion got cross with DS etc. DP is actually a lot better than me and never shouts etc, but it just raised my mummy-tiger hackles if he would ever use a slightly firm tone of voice with him for a while, and I would also always feel massively attacked if he ever expressed a tentative opinion on anything to do with childraising which slightly disagreed with mine. That was definitely something I had to work at, and he had to work at finding his comfort zone, him being thrown in rather a few years earlier than he was expecting with someone else's toddler, rather than starting from scratch with a tiny baby, but we talked about it loads before he ever got to the stage of being actually in the role of father figure, and though we have differing opinions on some things, they are similar enough not to cause friction, and we are both okay with the things that the other is not willing to compromise on (which, TBH, are few). Even though DS is mine and DP has never tried to insist I change anything I do with him, it's a possibility that we might have more children in the future, so I wanted to sort it because of that, and also, it's just nice to know that he agrees with what I am doing and isn't silently simmering about how badly I'm dealing with something, or whatever.
I think if there are DC involved you also need to be 100% sure this is longterm. You don't really get a trial shot - if he moves in and then moves out again later, that is going to be really unsettling for them, so you want to minimise the possibility of it happening as far as possible. Do you see yourselves getting married in the future? If he asked you now, what would you say? And the completely opposite topic - what do you think he would be like if you did split up? Would it be amicable? Would he still want to see the children? Are you able to talk about "what would happen if we split up" without it descending into insecurity about whether you are going to split up or not?
You might have been doing this already, but have you been on holiday together yet? Stayed at each others' for a weekend/week (with children)? I think it's definitely worth doing this, of course it won't give you a true idea of how things will be, but any major glaring issues will come to light, and it means you don't have to explain anything to the children if this does happen. If you have done this, were you both on best/trying to impress behaviour? You need to do it where you both relax as well, and act exactly as you would in your own home (with him taking the children into account as well, of course).
As for how long - I would say at least a year, we waited 10 months though so I'm hypocritical! But it just felt right. The things above were things that we went through (a million times... I am a worrier!) before anything happened. Housework we didn't actually discuss massively, but his standards are higher than mine, and it sorted itself out - we have an arrangement where he's in charge of the kitchen, hallway and our room, and I'm in charge of the living room, bathroom and DS' room. Actually we are both pretty crap in general 
but it's actually cleaner now on average than it was before he moved in, and it doesn't feel like one of us is doing all of it. Financially, we worked out how everything would change etc, but in the end it actually happened rather quickly due to family stuff, and what we completely forgot to take into account was that income support and tax credits stop straight away, and can take weeks to sort out the new claim, which meant we had just about enough to cover bills and a small amount of food for about 2 months, sounds fine in theory, difficult when you need to get a bus somewhere, or family emergency means you end up using more petrol than usual, or your toddler is going through a growth spurt and eating you out of house and home. If we'd have thought about that, we would have made sure we had some money as backup - in the end we just ended up asking our parents to buy us food, which was embarrassing.