funnily enough I also had an issue with Qatar at Manchester. I have a Non Immigrant O and the guy at check in was not going to allow me to fly without an onward flight from Thailand. I explained what a non immigrant O visa was but it was pointless. I asked to see the supervisor and luckily she know what she was looking at so problem was resolved.
with a one way flight you need to check with your airline if they will alow you to fly. A couple of the airlines need you to show proof that you are going to leave Thailand in the 60 days.
Check first and then you won't have any issues on the day you fly.
Hua Hin have a great immigration office. You can get the information you need from this group and then get the visa extensions at Hua Hin.
The easiest way to go is apply for a Non Immigrant O visas in your home country this will require that you can both show the equivalent of 800k each in your own bank account. Once you come to Thailand you open a bank account and if you can maintain that 800k each in your Thai bank account in the first 15 months of stay the Non O route is the best way to go. Note you can let the balances to drop to 400k each during that period but if your mindset is we need to leave the money in the bank that is the best way.
In Hua Hin the best bank to use for your visa requirement is Bangkok Bank. They have two excellent branches that I have personally used. One in Blueport Shopping Mall and the other just outside Market Village Shopping Mall. Both will provide you with any financial documents you need for your visa. Other banks can also provide you with the correct documents but not as efficiently as Bangkok Bank. I personally have accounts with 4 other banks and my experience is that Bangkok Bank is the best in Hua Hin.
Beyond the first extension. You will of had your original Non Immigrant O and extended for one year by then. Depending on you income you can reduce or eliminate the lump sum needed in the bank. If your income is over 130k Baht you can both use the income method for your future extensions. If your monthly income is above 65k you can use the income method for one of you and maintain 800k for the others extension in a Thai bank.
There is other visa types but Non Immigrant O is most straightforward. Others have mentioned the Non Immigrant OA. This is an option if you are going to to get health insurance and maintain it,. If you are a high net worth couple then there is a 10 year Long Term Resident visa you can apply for.
I have given you a high level overview. There are more details to each of the visa types which you can get from this group. As for hiring an agent there is no need to do that but if you really don't want to be bothered with applying for a visa extension once a year then choose your agent very very carefully. A bad agent (plenty around) is worse than no agent at all. I personally couldn't recommend any of the agents in Hua Hin as I have never personally used them.
for putting their head above the parapit and stating a price and what they are going to do for that price. I hope that I will never need assistance with my visa but if I did I would use these guys.
If people think opening a bank account is going to go back to what it was a couple of years ago I think they are very sadly mistaken.
how would you possibly know if you are not in Thailand? Can you read the SMS messages that are sent to the Thai mobile number the bank has for you? Can you physically receive mail from the address you gave?