As an experienced property manager, I have no qualms about one-bedroom units. Steering clear of them is outdated advice in my opinion. 

One bedroom units are very popular and easy to keep rented to single people and/or couples, because they are usually a relatively low cost housing option. They experience much less vacancy that a 3/2 home, for example. 

I do, however, have qualms about leasing to homeless or near homeless individuals (veterans or otherwise). Let me be clear: I am a retired military veteran myself with 22 years of service, and I do think it's a noble and honorable idea for you to want to help homeless veterans with housing. 

But I am also an experienced property manager with experience with the VA's VASH program, as well as similar programs for non-veterans. As such, I have grown jaded over the years and can tell you that in my personal experience 90% of these tenants don't work out. Often due to non-payment as soon as their benefits run out, and other times due to drug and alcohol abuse or mental health issues.

Just make sure you aren't looking at it through rose colored glasses, and understand what you are getting into. Managing tenants on these programs requires 2-3 times as much staff time and energy as managing a normal class B to C rental, and these units will very often experience much higher vacancy, collection, and eviction-related losses. 

That doesn't mean you shouldn't do it. These are just the cold hard facts.