
Hi Helen,
TBH I've always let pups have "access all areas" (supervised) from the outset because otherwise, IME, when introducing them to new places within the home they don't know how to "ask out" - i.e. where to head for :)
I'd suggest you just keep an ever watchful eye on the puppy - accidents are always our own fault (I've had plenty of them myself - erm, with my dogs that is

)
The running around the new environment within your home is almost certainly down to over excitement and best that you remain as calm as possible and try to distract the puppy with an organised behaviour - a calmer game with a toy, a few brief lessons on basic training such as sits/fetch/paw/down etc - mental stimulation tires them out more quickly anyway :)
The widdling when meeting strangers can be nervous/submissive behaviour (which doesn't sound the cause with your puppy!) or, again, over excitement. It will pass with age and development of bladder control which is really an ongoing learning curve for many months.
I would
not recommend going down the route of training your pup to paper or pads - all you're doing with that regime is encouraging her to "go" indoors - she wont make the connection that it's just a temporary measure. Go back to basics with her now and let her have free access when your around to other parts of the house - watch her like a hawk and any signs of sniffing or circling then gather her up quickly and take her out. Within a week or less she'll have worked out what best body language she uses to catch your attention whatever area of the house she's in :)
HTH, Teri