The oil heater I use in the kids room needs a three foot circle cleared. The ones I have in the pump room on a frost thermostat need a foot cleared. I don't have a radiant space heater per say, but have a 100W panel on the piglets. The front throws the heat an I don't think I could start a fire with one.
Now, the old milk house electric heaters I used would start fires if anything got five feet in front of it. An I had the auto shutoff fail when one got knock over. I was lucky I was in the shop when it happened or I'd lost my shop.
Measure the room an figure out the square footage. Then google how to heat it cheap an safely. I bet an oil filled is near the top.
Good luck!