By the house because you are a man, you want to own your own home and have your own space. Buying it primarily to benefit your game will be a let down (but I'm pretty sure you knew that).
Re: Game. Having a house usually doesn't hurt (unless it's a dump, or in sh!t neighborhood or you are constantly remodeling and ripping stuff up). Most women will see this as a positive because they read it as you being more stable, having at least avg wealth, independence, etc. Add in what the last poster said, when you have a home (and no roomates) women will be more relaxed.
Which brings up a related point. These women may get a bit too relaxed! They start picturing themselves living in your house, wanting to paint and decorate, etc. If things seem really good in your house, any intelligent woman will see a better place to live for less - "moving in together". Don't do it. Have a bud move in before you let a woman move in with you. Save that for getting married (if you ever do).
Also, if you are going to be spinning lots of plates remember once you bring them to your place they know where you live and have a lot easier access than they would in a more secure apt building.
Remember this too, moving into a home often means changing locations by several miles. I think it's just fine, but this can change the game for some guys as now they have to drive home several miles after going out when before it was short walk or taxi ride.
Another way to look at it, your first priorities should be yourself, career, home, family, friends and hobbies. Getting a house sort of forces you (at least temporarily) to put your home before women which isn't such a bad thing.
Best of luck. Owning a home is a great accomplishment and responsibility.