Just in case.Ultimately whatever correlates with your future plans but a solid way to build long term wealth.

My investor clients are typically happy with a small return right now but are buying on the idea of refinancing and getting future higher cashflow, principal paydown, and appreciation. 

We're new to real estate and would appreciate advice on our current home in Texas and our future place in Oregon.We love our house in Austin and aren't ready to sell, but as a long-term rental, it would yield (from what I understand) negative cash flow, covering principal and interest but not taxes and insurance.

Although whichever option you go with make sure you're also thinking about the long-term property value and what makes the most sense vs trying different angles now that negatively impact future resale/property values down the line. 

It is cheaper then FHA mortgage insurance, and you can potentially drop it in the future without refinancing unlike FHA. 

Be rid of the toilets, trash, liability and management headaches.5) Liquidity and Diversification: Diversify your capital into multiple real estate markets, REITS, stocks, bonds, multiple funds.

Real estate is not the stock market and it's called buy & hold and not buy & sell for a reason.I did sell a few properties about 10 years ago when I learned the hard way that going into cheaper neighborhoods was not the right strategy for me, so that was basically a strategy correction and it was necessary, but also costly both in terms of dollars and time.

I'm glad to see there are possibilities to invest remotely.We are considering a future project in the United States, specifically in Florida, Texas, or California.

Mind you, with mortgage interest rates in the US being so much higher now (and seemingly for the foreseeable future), I wouldn't be surprised if LTRs in Europe would cash flow better than in the whole US nowadays (to be verified).This being said, I don't and would never invest in LT rentals outside of North America  as I wouldn't want to face unfavourable landlord/tenant laws as a foreigner.

If you buy the single now your DTI will be negatively affected for future properties.