I love this post. It's a great idea. Plus I love rentals, and math.
I'm gonna quibble on some numbers, but in the end, it should actually come out in your favor.
Your numbers are pretty good (really close, actually, but I'd like 'em even more accurate, if possible.)
You shouldn't purchase if the rent isn't at least 1% of the purchase price per month (investors shoot for 2% or more, though that's often on multifamily; this is known as the 2% rule). So you should be getting at least 1800/mo rent on a 180k house. If you can't rent it out for 1.8k/mo, you shouldn't be purchasing for that much.
So in your numbers we can either tweak the house price down to 150k (and 1500 rent) or tweak the rent up to 1.8k. I prefer the former, as it may be a bit more realistic for some reasons I don't feel like typing up, but go with me on it? :)
Second: all expenses, etc. will add up to approximately 50% of the gross rent. If you self manage, you can take off 10% management fee. In this case, I think that's fine to do (but keep in mind that it's not a return on investment, but a job you're paying yourself for).
That should cover the maintenance, vacancy, insurance, taxes, capital repairs, etc. etc. So let's budget 40% of the gross rent (again, assuming self managing) for that. 1500 rent = 600/mo for those expenses. Many months you'll have leftover, stick that in an account for when maintenance, vacancies, etc. hit.
So on our house (that is now 150k), we'll put down 20%, or $30,000, and finance the rest ($120,000) at 3.75%, 30 year. Monthly payments will be $556.
Purchase the tumbleweed home for 20k.
Total spent: 50k (30k downpayment, 20k tumbleweed home).
That leaves 50k. I'd leave about 5k of that liquid, earning 1% (or $4/mo) for emergencies. This will build up as you take excess of that 600 and put it away for maintenance and vacancies.
I'd put the other 45k into whatever your comfortable asset allocation is. Let's KISS and say you get some dividend paying stocks that generate 4%, or 150/mo.
Monthly income:
1500 rent.
$154 interest.
Monthly expendatures:
600 maintenance/vacancy/insurance/taxes/etc.
556 mortgage
I would also get a home warranty in this circumstance. Most of the time I wouldn't recommend it, but since you're cutting it so close and the house is your main (only?) form of income, it'd be a form of insurance for any problems with the house. About $400/year. Put in your lease that tenants pay the trade service fee (usually about $60) when there's a problem.
That will run you $33/mo.
That leaves you $465 for everything else. If we assume 250 food, like you did, that leaves the "other" at 215 (real close to your 200).
Like I said, the numbers are close, but I wanted to get them a little more clear.
Health insurance is a potential issue. And doing this you're basically saying "I can live on a budget of $465/mo, or $5,580/year if I have no housing costs and my utilities are covered." That's tough to do.
This is a fun thought experiment though.