Unanswerable without the big picture. Will the $350K be a potential additional investment into an already substantial 7-figure+ diversified low-cost portfolio, or will it represent all or most of your investable assets? In the latter case you're taking a huge risk by placing your money into a single asset type, in a single location. That's the antithesis of a bedrock investing principle, which is to diversify investments to reduce volatility and risk. If the former, and you don't already own other real estate in some form (REITs, rental properties), you may be actually achieving greater diversification by increasing your present portfolio allocation to real estate, even if only in the form of a single property. That said, the risk with that particular asset will still be higher than the risk profile of diversified index ETFs or mutual funds. As long as real estate is a relatively modest component in a larger diversified portfolio, adding to the percentage allocated to real estate isn't necessarily a terrible choice.
All that notwithstanding, it's usually a mistake to view a principal residence as an "investment". It's a place to live, which is incidentally subject to movements in the real estate market generally and in your area more specifically. Treat your investments as such - liquid, diversified, low expense, long-term, and consider your residence as exactly that a component of your lifestyle, not as something acquired primarily in the hope of making money from it at some future time. For that, with real estate, look at REITS or rental properties if you think real estate is attractive for its investment potential as compared to alternatives which are more liquid and less management intensive (many professionals do not).
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