How do I randomly Spawn a home, Belonging to the Player, at game start?

Hey guys,

I'm in the process of creating my first Roblox game, so I'd greatly appreciate any help.

For my game, I want the player to have their own home (similar to games such as Meepcity and Pizza Delivery) that spawns at the start of the game in a random position. The home must never spawn in the same position as another player. Their will be a fixed amount of random positions based on the number of players that can join a game - say 10 players.

I'd like the home to have the player's name above it, too. When the home spawns, it must remember exactly how that player's home looks as they will be able to decorate it how they want, and buy items to go in it.

How would I go about setting this up?

I hope this makes sense, and I'd appreciate any assistance as I strive to become more familiar of how Lua works and Roblox Studio.

Thanks a lot in advance.