Buy a cheap temporary house or rent an apartment for way more money monthly?

In my area the only apartments under $1,500 are literally in the ghetto (un-safe areas), poor quality & noisy neighbors. The cheaper houses (for around $130,000) are in similar areas, but not aaas bad, and at least we'd get our own space, parking/garage, privacy, etc.

Between me and my fiancé we make around 50k a year, but still not enough for the kind of house we want (location & size) so we still need to save more for the down payment (In about 2 years), but we need a place of our own asap (and we have a dog so it's been very hard to find any apartments in our budget that allow dogs).

What would save us more money & be more convenient, getting an apartment in an undesirable area (where we don't even get private parking) for $1,500 a month + utilities, or purchasing a house for $135,000 which would equal monthly mortgage of $724 in my area (we have enough for down pmt & closing costs) and selling in 1.5-2 years? We don't care to make a profit from it at all, just as long as in the end it saves us even a little bit of money compared to renting an apartment.

Or… How do I calculate how long we'd have to live in that specific house before selling to break even OR not lose more than $10,000 in the end because that's still cheaper than renting the apartment.

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