It depends what you'll be doing here - if working, ask your employer to sort out a work permit and visa - if studying, get a visa through your college/university - if you're so rich that you won't be doing either, buy an Elite visa.
If I understand correctly, their system should show as you not having overstayed, so you don't owe anything.
I had the opposite where they stamped me in for an extra month by accident, which I assumed as being intentional, but I had to pay for a month's overstay on my way out because it's what's in the system that takes precedence.
For peace of mind, the Elite visa would be the best option. With annual renewals, you would always be at risk of unfavourable major changes to the renewal / extension rules, which is quite likely over time, given that Thailand is still a developing country beset with political instability.
It's very unlikely immigration will bother you (unless you upset someone enough to report you) but getting caught would almost certainly mean being deported and blacklisted, which isn't worth a few peanuts.
UPDATE: as suggested by some of you (thank you!), I got a copy of the chanote document from my landlord and the embassy accepted it - they processed my visa swiftly thereafter.
yes, I definitely should've just booked at a hotel from the start - it was just that on their website it says house registration "(if any)", which I wrongly understood to mean it's optional