I knew my girlfriend through work before she even split with the dad so obviously I was fully aware she had kids, and she spoke about them a lot.
When we got together I was 37. I had no kids of my own because my previous long term girlfriend hadn't wanted them. I wasn't bothered at the time.
When we split I partied a bit, then got my head together, and felt very regretful that I didn't have any.
I spoke to my girlfriend a lot between her splitting with her ex and us getting together. I knew the deal. Because the kids were so much a part of the girl I was falling for it was never a problem. I do think that these conversation became something of an interview process for her though - to see if I was the right material. Her ex (who isn't an evil man, just plagued with issues and unable to connect with the kids) had never been able to give her the family dream she'd wanted.
The girls were 2 and 6 at the time, so still at a very adaptable age. I'd have been far more intimidated by young teens, to be honest.
We introduced me as mum's friend and when they saw me it was largely me and the six year old running round a soft-play area having fun. The 2 year old seemed relaxed based on her mum's enjoyment of me being there, and the fact that big sis wasn't taking some of mum's attention!
But to answer a couple of specifics:
"Taking on another man's children": The dad and I are two very different people, although we get on pretty well. It was important for him to 'sow his seed' but the day in, day out routine of raising kids was something he had little interest in. He was genuinely surprised when my girlfriend told him he should have an active part in this - his own dad didn't and he didn't think that was how it worked.
I had always been keen on adoption, as a very compassionate act, and never saw that the lack of some of my genetic code would be an issue in how much I could love a child. But I take joy in the day to day life of it, and the 'family' events and all that.
I do think it's different for men - we ejaculate and wait nine months, to be blunt. Meanwhile the mother is growing and nurturing the child, and for nine months is joined in a way that we'll never comprehend.
"Maturity":
I suppose that's just something you have to get a sense of. My ex had been frequently depressed and during this time I had to do pretty much everything - housework and administrative stuff. I suppose my gf at least could see that I'd had to be responsible. There was still no way she could be sure though.
It's always, always going to be a gamble I guess. In some ways I'd say any man you might meet will have it slightly easier since the dad isn't on the scene. My SDs see their dad for two nights every other weekend, and like every Step Parent I tread the tightrope of "when do I get too deep and step on dad's (or mum's) toes?" It's a stress that is always there basically. I've had SD7 telling me she misses her dad but is happier with me there. Lovely? I hate that a 7 year old even has to think in those terms, and what is best for her then? For me to refuse to engage on the topic because it's not 'right' for a SP to talk to them on that level? I settled for telling her I was happy but remember all the wonderful things Dad does for her and how special a dad is. The tiredness, lack of personal time, occasional bad behaviour - all that is part of the experience I'm loving every day. The balancing act of doing the 'right amount' as a step parent is the knackering part!
I hope that answers some of it. I'm a little sick at the moment (I don't quite have a real parent's immune system yet :p ) and fear I may have rambled...