First, I’d say you need to do some research on both adoption and surrogacy and pick which one is right for you. You won’t be able to do both at the same time.
I considered surrogacy but on the balance of our ethics/beliefs, discounted it however, I have a friend who had her daughter that way.
Their experience was that it was stressful, and the child wasn’t legally theirs for a long while which was unsettling however, a genetic link was very important to them and they don’t regret it at all.
For adoption, I’d say learning about trauma and its effects on children is essential. Children don’t know when their birth family are neglecting them etc, so they feel the loss of what they know keenly, even when they’re tiny. That goes for children removed at birth up to
children old enough to remember their birth families.
For your pets, they will be assessed as to their suitability to be around a child. As PP said, it’s not just a case of assessing a dogs behaviour, it’s about what happens if a child falls on them/doesnt understand how to handle them and hurts them? Probably not something to worry about at this stage though.
As a first step to adoption, I’d look at your local council. Ours held information days where you could ask questions. That and reading up on attachment and trauma was our first step.
Once you’ve decided to do it, you contact the agency and they’ll guide you through the process.
The process itself is intrusive. They will talk to your friends/family/employer, check your finances, background for convictions etc and ask personal questions about your life, health, relationships, beliefs. It can be a bit uncomfortable but nothing major and it’s 100% worth it at the end.