I started by talking to my bank (a credit union) to get pre-qualified. I recommend it as a first step. They will tell you how much you are qualified to borrow, which is not necessarily what you can afford or would be comfortable with. Keep in mind insurance and taxes will be needed along with the monthly mortgage payment. My credit union had a first time homebuyers program which was a huge help. I can share more details about that if you’re interested. Plenty of old timer agents will jump at the opportunity to take advantage of a first time homebuyer.
Once you are pre qualified, find a real estate agent. They will help you with the rest. Do your research and be skeptical of the big local firms. I found an agent who worked in my town occasionally, but wasn’t part of the local political circlejerk (it’s small city in the south but I’m sure this is an issue everywhere).
I’m glad your dog is ok and the neighbor seemed to learn their lesson. Too bad it had to happen like that. When OP said “in other countries” dangerous animals attack cats I immediately thought of dogs as a threat to cats anywhere. We are in the US in an urban area and there are also owls, hawks, tics, poisonous snake, all which pose a potential threat to outdoor cats.