First, determine your objective. And while it may be clear in your mind, it's not clear from the question. For example, you ask about buying a home for investment. There are 3 possible goals: (1) Cash Flow, (2) Instant Equity; and (3) Appreciation.
The three are not mutually exclusive, but you may find it difficult to get a good balance of all three.
Let's consider each:
Cash Flow: This is mandatory. And so your statement about "best chance of breaking even" worries me. First, don't take chances. Know your numbers going in. Second, don't ask about your "best chance of breaking even." There's no cash flow in breaking even. So, regardless of how much emphasis you put on points 2 and 3, your question must be "How do I find a property that will have a positive cash flow?"
Answer: You work the numbers, keeping your monthly outlay low and maximizing your income. You keep your monthly outlay low buy buying right--not overpaying--and having financing or an arrangement that keeps your costs low. In fact, you might not even have to--or want to--buy. You might be able to rent on an annual (or even multi-year) basis, then sublease on a weekly basis. You'd want to check all appropriate regulations and make sure the lease you write permits this. But that way, you could get a nice positive cash flow simply by being an intermediary and marketing the property you're renting. Again: Check all appropriate regulations. And that's just an example of one of the ways you could do it without buying. Another way: Lease-option. You'd do the leasing end the same as described above, but with the option you could take advantage of any appreciation.
Instant Equity: You buy at a below-market price. You still need positive cash flow, but now you're building in some paper profits from the beginning.
Appreciation: This is a gamble. Unless you plan on holding for 15-20 years or more, don't assume there will be appreciation. And even then there may not be. Folks who bought in Detroit or other areas of the Rust Belt 20 years ago often haven't seen any appreciation. Appreciation is the frosting on the cake. Now, by choosing the right property in the right area you can increase your chances of appreciation. But I know plenty of investors who are making lots of money on properties that aren't appreciating at all. They'll buy an urban rowhouse for $30,000, then rent it out for $650 a month. They don't care if its value goes up a penny.
Look: I know you were hoping for an answer like: Buy a 3/2 rambler, then convert it to a short-term rental. But that's really not the way to look at it--not if you're really looking for an investment.
Hope that helps.