Your visa has no affect on whether or not you can own property here.
However, do not buy a condo you haven't stayed in first. Most Thai developers don't really focus on quality and long term sustainability, but on flashy exteriors and cutting costs. Renting is also safer, since the property market in Thailand is suffering from an overabundance of empty units just wasting away, with owners refusing to lower the prices to sell/rent.
But if you really want to buy, stay in a condo for a year. Get to know the building and ask your neighbors who bought what they think, before you buy a place yourself.
I've used Safetywing for a year and a half. Works great , made 5 claims this far and never had any problems, unlike Thai insurance companies that fight you for every baht.
Safetywing covers you in Thailand, but also the rest of the world, in case you travel a lot.
It's very common to ask for a booking fee, to hold the condo for you. Since you haven't signed a contract or paid a deposit yet, it's a safety for the owner, in case you cancel. You then pay the rest on the day you sign the contract or on the day you move in.
If you're looking for a condo in Pattaya or Rayong, let me know and I can help you out.