Hi Shelly. Sorry about your running injury. If you're not interested in leaning over, you don't want a road bike or a mountain bike. From what you describe, you probably should look at comfort bikes.
These have fatter tires than road bikes, but may or may not have as rugged tires as mountain bikes. You sit up on these type of bikes.
When buying a bike, you pretty much get what you pay for. If you buy a $200 bike at a box store, you're not going to get much in the way of quality. Plus the bike will probably be quite heavy.
That's the next thing - the weight of the bike. Bike frames come in steel, aluminum, aluminum with carbon components, and carbon frames. I don't know if they make comfort bikes in carbon frames, but I am thinking probably not. Carbon is used more for racing. Steel is going to be very heavy meaning you will really have to work at pedaling the bike. Most folks go with aluminum which is lighter.
As far as any bike needing cleats, that's a personal preference. People change out pedals to have a flat pedal, one with cages (not recommended for safety reasons), or with cleats (also known as clipless pedals). You can have a flat pedal or cleats on any bike.
If the owner doesn't know anything about their bike, then I wouldn't bother with them. I am not an expert by any means, but at least I know what material is used in all of my bikes' frames (I have 3) and I know they all have Shimano components. I can't tell you which line these components are, but I would guess not the top nor the bottom of the line.
The Rhino Mountain Edge sounds like a mountain bike; I couldn't find a picture of it online. I also couldn't find a price for it, so I'm thinking it's a bottom of the line bike. The little bit of research I did on the Roadmaster is that it's a very cheap and unreliable bike. I would stay away from those two. Magna I think are also bottom of the line bikes and you may want to stay away from those. Schwinn's quality varies; it depends on the model and year.
Good, dependable brands are Trek, Scott, Cannondale, and Specialized. I'm not sure what your budge is, but you should be able to find something decent in the $400-$500 range. Here's a link to some Hybrid Bike Reviews; you can sort by price, but you'll have to click down to get to the cheaper bikes.www.roadbikereview.com/cat/latest-bikes/hy
One more thing I would add is to get your bike from a bike shop rather than a box store. You'll get good advice, have your questions answered by someone knowledgable, get fitted properly on the bike, and you'll also be keeping a local neighbor in business rather than a giant corporation.
Enjoy shopping! Let us know what you decide upon.
"God gave you your body as a gift, so you should take care of it." - My Mom