I have read/heard that it's best to start "in your own back yard" to get the feel of being a landlord/investor, but when my backyard isn't the most fertile soil, I may need to cast a wider net.  

Linoloeum has been around far longer than vinyl and when vinyl appeared on the scene in the 50s/60s, folks continued to refer to the roll/sheet flooring as linoleum.Linoleum is frequently used in commercial settings such as hospitals, care homes, daycares, schools as it wears well (colour is all the way through) and is naturally antibacterial - we recently bought a house built in the 1930s which still had the original linoleum underneath vinyl loose-lay fibre floor in one of the kitchens ... the linoleum was in better shape than the vinyl.These days linoleum is a little more expensive than vinyl, but comes in lots of fun, funky colours and patterns {Google Forbo Marmoleum to get an idea}.  

Some areas near Niagara and Buffalo have very poor soil which means there are going to be foundation problems and I would not be surprised if the people come down with cancer because it was used by the military for disposing hazardous material a long time ago. 

What's the soil like?

I read up a bit on this and I think the last thing I want to do is repair an old stucco house built on clay soil, with a slab foundation, even if it's real stucco.

In localities having a winter design temperature of 32°F (0°C) or lower as shown in Table R301.2(1) of this code, a water, soil or waste pipe shall not be installed outside of a building, in exterior walls, in attics or crawl spaces, or in any other place subjected to freezing temperature unless adequate provision is made to protect it from freezing by insulation or heat or both.

If it's in a great area, there are no major, deal breaking issues around the property (soil/foundation issues etc.), and you can rehab it without breaking the bank, i would say it warrants a more detailed investigation.

Best bet it to make your offer contingent upon a soil test.

They strongly recommended removing the tank so that the soil could be tested & cleaned if necessary.The agent for the seller refused to consider this & my agent considered it overkill.

On the other hand, if your supply valve/hose breaks underneath your sink, or your tub overflows, it's the units owner's responsibility.