โธมัส เมห์ลฮอร์น I also use Phetchaburi immigration and have done since 2016. The rules changed 1st March 2019. I have attached a translation of the actual police order that instigated this change.
If you have been in Thailand continuously since before October 1998 you could qualify to have a lesser financial requirement.
Practically to stay in Thailand long term you will need to apply for a Non Immigrant O visa. You have at least 2 options, maybe more after advice from the London Consulate:
1. Supporting your Thai child.
2. Being over 50
When it comes to extending your visa in Thailand. There is more paperwork required for supporting your Thai child but the financial requirements are less.
You may find you extend your visa using both methods. Initially maybe supporting a Thai child and then later on being over 50 (retirement) later.
You mentioned about a few visits to immigration as possible. I live in Cha Am and although Hua Hin is not my immigration office I have had a few dealings there and they are a pleasure to deal with. The best tip I can give you on Hua Hin is go to the phitocopy lady on the ground floor. She will make sure you have all the correct paperwork in the right order. Dress smart casual and have a smile on your face and you will be fine.
When it comes to choice of visa.
O-A is a good option if you are going to take out medical insurance.
O based on being over 50. Is the easiest option based on the ammout of paperwork. But requires more money deposited in a Thai bank. If your income is more than 65k a month you can use that to extend your visa in the future.
I based on being married to a Thai National. There is a high ammout of paperwork for this and when you apply it takes at least 2 visits to immigration to get your yearly extension.
O based on supporting a Thai Child. This may be a possibility depending on the age of your Thai son or daughter. Paperwork will be similar to that needed for the married to a Thai national. Financial requirements I believe (please check) are 200k seasoned for 2 months before you apply.