You weigh everything very carefully. That is certainly not a bad thing. Within the framework that is affordable, it’s also about a feeling of life. Which makes you feel better, renting (and waiting) or living in your own property? The annoying thing about the future is that you can't predict it very well. You can only make the best possible decision right now.
I find children’s noise hardly annoying or not annoying at all. For me, it is not "negative" noise. What bothers me more are a quarreling couple of neighbors, the dreadful lawnmowers, cars with running engines. That is "negative" noise, associated for me with negative thoughts.
I definitely wish you a burst of joie de vivre and courage to decide, even if you can’t know exactly what the best decision is. (see: afterwards you always knew it in advance – Horst Evers).