Reviewing my specific first-purchase numbers (low DTI, modest income, small down payment, high rate) — is this a good idea?

On the numbers, this looks solid. The rate and your time horizon are the two things worth a second look. A payment around $1,200 to $1,300 on a $158,000 home, plus roughly $700 of other monthly debts, against $6,000 of net income keeps your debt-to-income comfortably low. That is a good place to buy from. The flag worth chasing: a rate near 7.75% on an FHA loan with 3.5% down looks high. FHA allows 3.5% down with a credit score of 580 or above (scores from 500 to 579 require 10% down), so a rate like that usually signals a score sitting close to that 580 floor. If your score is actually in the 640-plus range, FHA pricing typically comes in meaningfully lower. Those figures are illustrative rather than a current-market quote, but the gap deserves a look before you lock, because a better score can move your payment. The bigger caution is time horizon. With 3.5% down and FHA's upfront mortgage insurance premium financed into the loan, you start with very little equity, so there's a real stretch where you could owe more than the home is worth if prices don't rise. That's fine if you plan to stay put for a good while, and riskier if you might need to sell soon. Tune out the market doom-and-gloom and focus on whether your finances and your life are stable enough to hold the home for several years. If they are, this is a reasonable first purchase.