The Player's Handbook assumes the characters have expenses of the lifestyle they choose that have daily costs. But if your player really wants to own a house you can adjudicate a buying cost that will be a resonable number for your campaign. This will go into the zone of house rules but you are the DM, you can decide what is the best price for a house in the small town that adventure takes.
All in all I'd say 200. One of them wants to buy/ acquire his own tower as a home and is asking me how much it is going to cost. I swear one of the rule books had information for players trying to buy properties, but I cannot find it on DND beyond.
Browse and reference your favorite RPG rule sets for systems including D&D, Pathfinder, Call of Cthulhu, and Cyberpunk RED. D&D 5e handily gives you a chart of the cost to maintain a certain standard of living, split into housing (if you're renting a room), meal costs and 'other'. I'll reproduce it here, so you can see what buying a house saves you on rent and food costs (in case of a farm or manor).
Buildings are structures that are constructed for urban use or for other reasons. The prices listed generally refer to construction or purchase. However, it's difficult to sell these buildings in undesirable areas, such as those infested by monsters or other hazards.
My players have gotten to a point where they're looking to buy property and I wasn't satisfied with the lack of details to help me figure out how much property and buildings should cost. So, I was inspired to make a property buying system in dnd that took out most of the guess work! The costs found in this guide are based on the DMG. Probably over that, since those calcs didn't include the cost of the land.
Although a house in a city won't have as much land as a country manor, it's probably worth more per area, especially in a city's most exclusive neighborhood. You're probably looking at something closer to 75,000-100,000 gold pieces. The south of the Khanate of Barbi is unclaimed territory! Town building there should be easy, and the Pioneer cost is low.
Let's see what it costs to make a profit in DnD 5e! Rules and info for pioneers for the Southern parts of the Khanate of Barbi: (We are Beta testing this.) Overview The Feudal Contract The Khanate of Barbi Leadership and growing a pioneer population Building Your. It uses the building costs from the Dungeon Master's Guide as a base; check out the building rules from the HyperText d20 SRD. A D&D 3.5 House Rule.
Buildings I based everything on a cost/square foot figure for each building type and material, and expressed upgrades as additional costs.