I'm a HR manager and I would hate, hate, hate anyone to tell me during the recruitment process that they were pregnant.
Firstly, it is none of my business.
Secondly, I would feel that they were trying to trap me i.e. forcing me to offer them a job on the basis that if I didn't , it might look like i didn't offer them the job because they were pregnant.
Thirdly, it doesn't serve any purpose to give this information during the recruitment phase.
You are not obliged to share this information - it will not "cast a black cloud" over your starting with the company. Nor is it deceitful or a negative reflection on your integrity. Your pregnancy is personal private information that has absolutely no bearing on anything to do with the recruitment process.
Likewise, there is nothing to be gained by sharing the information after signing the contract but before starting. I recommend that you start in the company, and then whenever you are planning to start telling your family and friends you can consider to share the information with your new manager - explain to him/her that you didn't want to mention it until you had reached the second trimester and felt a bit more secure in the pregnancy. No biggie.
And, not to be pessimistic , you are very early days yet - there is the possibility that you could miscarry and then what would the point have been in sharing this information? (sorry!)
Any organisation can adjust to employees going on maternity leave - just like they adjust when people decide to leave the organisation.
It's absolutely no biggie if you get a job, then at 15-20 weeks tell your manager that you will be going on mat leave in 3 mths time. This is ample notice for them to make plans for cover. If an employee was leaving on the other hand, the company often only get 4 weeks notice so there is a mad scramble to backfill the role.
There is a tendency for people to act like a pregnancy is something wrong or shameful - you are entitled to be pregnant, and you are entitled to privacy around your pregnancy, and posters trying to push you into an early on the basis that not doing so would be unrespectable, or poor reflection on your integrity is just wrong.
Congratulations on the pregnancy and the new job.