In our market that usually means a larger property with at least one 3bd unit, you would occupy the 2bd with a roommate.  

House is your primary residence, so live there and take roommate(S) to help you pay down the mortgage.You can't re-evaluate the value (to order new appraisal) for 3 years to get new LTV ratio. 3% down is marginal anyway, you wouldn't get much cash flow after PITI and PMI anyway.Just live, save money for next one and play safe. 

It's not only about credit score and down payment, they are assessing your ongoing ability to pay given your other required payments.It could be perfectly reasonable if you hack it with some roommates, duplex maybe, and/or get a co-signer. 

Will you have roommates?

This way, if the tenant/roommate was doing nothing legally wrong but we just didn't mesh well, we were not contractually obligated to continue sharing our own home with this person.Overall, we had a great experience renting out rooms and it split our mortgage in half.

My max budget is up to $250,00 (5% down, 4% interest rate, 30 year conventional)I am most concerned with long term cash flow from the property and plan to hold it for a long time.My roommates work across DFW, so I am attempting to be as close to this sliver (west of Greeneville Ave., South of 635, east of 35, and north of 30).

If you're comfortable living with others, house-hacking a 4 bedroom (SFH) with 3 roommates could be the way to go.

I am living in an apartment with 2 roommates in Los Angeles, CA.

I have a roommate that delivers pizza and  the majority of his income is cash from tips.

For example I bought my house around 2013ish, the value has increased 150k, my mortgage is being paid 40% by roommate.