@Kevin H.
First, congrats on being financially responsible and getting yourself in a good position.
I'd recommend running the numbers on your paid off house as if you were going to buy it as a rental. Does it meet you goals? Just because you have no debt on it, does not mean its the right rental for you. Maybe selling it is the best option? You could then re-deploy the capital in other properties.
Doing real-estate without leverage is really giving up on one of its primary advantages as an investment. If you are cautious, try to get yourself to a place where you stick to low LTV - borrow only 60%. You can double your exposure and still be in a very low risk situation. Even in the housing bust, few properties lost 50% of their value.
I'm in a similar situation to you, I don't like leverage and I have my primary residence paid off. My resulting choice is to invest in the stock market and live without leverage. I focus on my consulting business to bring in more money. I am well educated about real estate, and I know I'm missing out on an opportunity for diversification, leverage and good returns - but I'm held back by my fear of leverage.
You need to decide: what scares you most:
1. stock market
2. leverage
3. low returns
If you are happy with low returns, do a low-leverage/no-leverage real estate investment. You'll still do better than your bank account and you won't have to deal with the stock market.
I think you should try to use 'some' leverage, but less leverage than is available at first.