It also includes managing your existing investment well to ensure you aren't bleeding money due to bad tenants, excess maintenance, etc. 

You want to make sure you aren't muddying the water and making the tenant think they have longer to get out.

Even if you aren't into creative finance, stay away from rough neighborhoods.

I know that the general guidance is that emergency funds aren't to be invested, but given our financial security and the fact that we already have a personal e-fund in a safe, non-volatile location, would it still be crazy/unwise to invest this 15k in an S&P500 index fund in a brokerage? 

If you're planning to buy in the US, there are programs for those that aren't US citizens.

If you aren't paying cash and are doing owner occupancy you may be able to use FHA instead of Conventional with a higher down payment. 

Those are spray and pray techniques that don't fit with sellers right now because sellers/owners are sitting on a very low rate and don't want to move to go up 4-5 points on their rate.Listings aren't a start now thing as well.

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.

You aren't offering any unique amenities.

Insurance right now is wild, so I'd get a solid broker on your team - I'd be happy to share my contact if that would help.Also, aren't most of the existing insurances shared on the OMs for the properties?